Virgin Trains, which operates across large parts of the UK, has posted a message in capital letters on its official Twitter account urging "all customers to abandon travel".
Earlier, Network Rail urged commuters not to travel after confirming that the West Coast Main Line will close at around 7pm for a couple of hours because of high winds.
The suspension was called due to high winds north of Preston and affects the section of track between Preston and Carlisle.
Network Rail urged commuters travelling from Glasgow to south of Carlisle not to travel. Customers with advanced tickets can travel tomorrow or get a full refund. Virgin has said it will not lay on buses during the closure.
Alternative services are available via the East Coast, where services are running normally.
Talks are currently under way to discuss whether the Scotland to London sleeper, which normally leaves Glasgow Central at 11.40pm and goes down the West Coast, will be diverted to the East Coast line instead.
High winds and snow have caused "carnage" on some Scottish roads, according to police. Warnings of high winds and snow are in place throughout much of Scotland.
The southern tip of Dumfries and Galloway is predicted to suffer from the same severe low pressure system that is causing major problems south of the border, although weather warnings are less severe throughout the rest of Scotland.
The worst disruption in Scotland appears to be on higher ground, including an accident in the Highlands involving a heavy goods vehicle (HGV) and a van, which left one man trapped.
Fire and rescue crews had to cut the van driver free after his vehicle collided with an HGV on the A9 at Drumochter Pass at around 2.20pm.
The drivers were taken to hospital but their injuries were not thought to be life-threatening, police said.
There was also disruption on the A82 at Ballachulish with a jack-knifed lorry and several other minor road traffic collisions, which did not result in any injuries.
Road users have been advised to use caution crossing the A9 Dornoch Bridge due to high winds, and the snow gates were closed at Cock Bridge in Aberdeenshire.
There has also been "carnage" on the roads in the Tayside area, according to a Police Scotland spokesman who has advised drivers to avoid the area.
Two HGVs collided, blocking both carriageways around five miles south of the House of Bruar on the A9 southbound. No-one was injured.
A Mercedes C20 car carrying four adults also slid off the road in the same area.
At 2.30pm, a lorry broke down on the A9 at Pitlochry with a punctured tyre.
The snow gates were closed in both directions at Calvine, in Pitlochry.
Elsewhere, the M74 southbound was closed at the Happendon Services, South Lanarkshire, following an accident at around 5.40pm.
First Minister Alex Salmond chaired a Scottish Government Resilience Committee (SGoRR) meeting this afternoon to assess preparedness across Scotland for the potential impacts of the forecast weather conditions.
The meeting, which involved the Met Office, Sepa, Transport Scotland and responder organisations, heard there would be an amber warning for southern parts of Dumfries and Galloway, three distinct Yellow weather warnings in Scotland overnight and into tomorrow morning, with the Red warning being restricted to south of the border.
Transport minister Keith Brown said: "The Amber alert for high winds in south-west Scotland this evening and the Yellow warnings that we have in place for snow and wind are to a certain extent reflective of normal winter conditions, but these still have the potential to bring some disruption to travellers in the affected areas.
"Road operators, train companies and those involved with ferries and aviation will plan ahead in the usual way and put in measures to mitigate any impacts, but given the conditions expected north and south of the border there are likely to be some impacts to cross-border travel, particularly on the West Coast Mainline, higher level routes and ferries on the west coast.
"High winds could also restrict road bridges overnight.
"Travellers should follow the tried and tested practice of checking all available advice before they set out on their journeys."
Environment and climate change minister Paul Wheelhouse added: "While the forecast does not anticipate the extreme severe weather forecast for Wales and the north-west of England to come as far north as Scotland, we cannot take it for granted that there will be no impact and therefore it is important that we are ready to react.
"We heard today that all our key stakeholders remain in a high state of readiness to deal with issues as the arise, and to respond quickly to any sudden change in conditions.
"They will continue to monitor the situation closely."
With further bad weather being forecast for the weekend, SGoRR is monitoring the developing situation and will meet again ahead of the weekend to update on the situation.
Elsewhere, the Thames is predicted to rise to its highest level in more than 60 years in some places, while the Met Office has issued a "red" weather warning for exceptionally strong winds in western parts of Wales and north-western parts of England.
Winds of 80mph are expected widely in those areas and gusts could reach up to 100mph in the most exposed locations in west and north west Wales, potentially hitting power supplies, bringing down trees and causing widespread damage.
Coastal areas could also be battered by large waves, the Met Office said.
Gusts of 92mph have already been recorded in the Mumbles on the Gower Peninsula, south west Wales, and the south coast of the Irish Republic has been battered by winds of 96mph, weather forecaster Meteogroup said.
The Met Office has forecast 70mm (2.75 inches) of rain by Friday in the already-sodden West Country - more than the region would normally get in the whole of February - with western Scotland, south Wales, Northern Ireland and other parts of southern England also expected to bear the brunt of the deluge.
Windsor, Maidenhead and communities in Surrey have been warned to expect severe disruption and risk of flooding. There are 14 severe flood warnings - meaning there is a danger to life - in the Thames Valley.
Around 50 homes flooded overnight in the Thames Valley, bringing the total number of homes flooded across the country since late January to 1,135. Some 5,800 properties have flooded since early December when the series of winter storms began.
Another two severe flood warnings remain in place in Somerset, while the Environment Agency has 129 flood warnings and more than 200 less serious flood alerts in force across England and Wales.
The AA said that by early afternoon it had attended 29 flood-stricken vehicles, with the number since last Friday reaching 680.
Prime Minister David Cameron will cut short his attendance at an international conference tomorrow to focus on dealing with the flooding.
He had been due to speak at the London Conference on the Illegal Wildlife Trade, alongside the Prince of Wales and Duke of Cambridge.
But a Downing Street spokeswoman said: "The Prime Minister will briefly dip in to meet with international leaders attending the event but his attendance will be cut short."
The new Cabinet committee on flood recovery will meet tomorrow, replacing a scheduled meeting of the full Cabinet.
Along with the Prime Minister and Deputy Prime Minister Nick Clegg, the committee includes Home Secretary Theresa May, Defence Secretary Philip Hammond, Communities Secretary Eric Pickles, Business Secretary Vince Cable, Transport Secretary Patrick McLoughlin, Treasury Chief Secretary Danny Alexander and Cabinet Office ministers Oliver Letwin and Francis Maude.
Chancellor George Osborne is also a member of the committee - although he will not attend tomorrow - along with Environment Secretary Owen Paterson, who is recovering from eye surgery and will be represented by floods minister Dan Rogerson.
Surrey Police said around 1,000 homes in their area had been affected by flooding, with 600 people evacuated.
"Latest forecasts indicate more rain is expected and water levels will continue to fluctuate over the coming days and into next week," a spokesman said.
With more rainfall forecast today, tomorrow and Friday, the threat of flooding is likely to increase of over the next few days, with communities along the Thames in Oxfordshire, West Berkshire and Reading, and along the Severn in Worcestershire also at an increased risk.
Coastal flooding could hit north west coasts and the Dorset coast tonight, while the threat of groundwater flooding continued in Hampshire, Kent and parts of London, the Environment Agency said.
Toby Willison, programme director, Environment Agency, said a number of rivers in the South East and South West, including areas of the Thames, were at their highest ever recorded levels.
"This is an exceptional event, it was the highest rainfall in January since 1776 and we think it is likely December, January and February will be the highest for 250 years," he said.
Environment Agency staff had to be withdrawn from the flood-hit Wraysbury area of Berkshire following abuse by local people for a short time on Monday, but Mr Willison insisted the agency had people back on the ground and said the response to the floods was a "real team effort".
Some 23 temporary defences had been deployed along the Severn and the Thames Valley, and 9,000 sandbags were handed out in Windsor last night, he said, with 20,000 more to be deployed in the West Thames area.
"There is a real concerted effort to ensure the impacts of this event are reduced as far as possible," he said. No flood defences had been breached, but there were places where they had been over-topped by the sheer height and volume of the water.
Major General Patrick Sanders, Assistant Chief of the Defence Staff, said troops were providing help with resilience, relief and additional manpower for what he described as an "almost unparalleled" natural crisis.
"There's more that we can do and we want to do more wherever we can make a difference, so please use us, that's what we're here for," he said.
And Peter Holland, Chief Fire and Rescue Adviser said all the country's fire and rescue services have been involved in supporting colleagues in the flooded areas.
In the Somerset Levels alone 21 out of the country's 46 fire services had been involved in the major pumping operation to help clear flood waters.
By this afternoon, gusts of more than 100 mph had been recorded, with winds of 108mph hitting Aberdaron on the Llyn Peninsula in north west Wales.
Off the south coast of England at the Needles, on the Isle of Wight, gusts of 96mph were recorded at lunchtime.
The M6 was closed in Cheshire, between junction 19 at Knutsford and 21A Croft interchange due to gale force winds with cross winds along Thelwall Viaduct, the Highways Agency said.
Major General Sanders said 1,600 troops had been committed, and thousands more were available if needed to help communities deal with flooding.
The latest swathe of appalling weather to hit the UK comes as a Government minister warned there was no "blank cheque" to pay for repairing the damage of weeks of storms and floods that have affected parts of the country.
Mr Cameron, who chaired a meeting of the Government's Cobra emergencies committee in 10 Downing Street, promised yesterday that "money is no object" in offering relief to those affected by the floods.
But Transport Secretary Patrick McLoughlin indicated that there would be "careful consideration" before money is spent on the larger rebuilding exercise of restoring damaged infrastructure after water levels recede.
"I don't think it's a blank cheque," Mr McLoughlin told ITV1's Daybreak. "I think what the Prime Minister was making very clear is that we are going to use every resource of the Government and money is not the issue while we are in this relief job, in the first instance, of trying to bring relief to those communities that are affected.
"Then we have got to do the repairs of the structures and the railway infrastructure that's been damaged and then the other long-term issues, which will need some careful consideration."
At Prime Minister's Questions Mr Cameron said grants of up to £5,000 will be available to businesses and homeowners hit by flooding to protect their properties better in future.
He also announced a £10 million fund for farmers whose land has been waterlogged for weeks and deferred tax payments and 100% business rate relief for affected businesses.
Mr Cameron repeated his pledge that "money is no object in this relief effort" as he was questioned by Ed Miliband about the Transport Secretary's comments.
A lorry driver is in hospital after high winds blew over his vehicle in Bristol.
Avon and Somerset Police have closed Spine Road, St Philips Causeway, Arnos Vale, in Bristol, in both directions as a "safety precaution".
A spokeswoman for the force said: "The decision has been made after the strong winds meant a lorry was blown over while driving along the road earlier this afternoon.
"The driver has been taken to hospital but he is not thought to have been seriously injured in the incident.
"Drivers are being advised to avoid the area until the road is reopened. It is unknown at this time when that will be."
The decision comes after the city's iconic Clifton Suspension Bridge was closed to vehicles this afternoon due to gusts of up to 60mph.
Officials reopened the bridge just after 2pm.
Residents of a Gloucestershire village who have been cut off for weeks because of flooding have received essential supplies by boat.
Parts of Tirley, near Tewkesbury, are under 5ft of water after the River Severn flooded and 18 homes at Haw Bridge have been cut off since Christmas Day.
A team from Severn Area Rescue Association was drafted in yesterday to take supplies of bread, milk, eggs and soup that have been donated by Sainsbury's.
A spokesman for the association said: "A total of 10 water rescue technicians attended and delivered food parcels to residents cut off by flood water in the Haw Bridge area.
"One resident requiring ongoing medical attention was assessed and arrangements made for planned evacuation with NHS supervisors."
The floods have forced a homecoming parade for soldiers returning from Afghanistan to be cancelled.
Some 200 officers from the 2nd Royal Tank Regiment were due to take part in the parade through Clapham Junction, south London, tomorrow afternoon.
But the event has been cancelled after the Government ordered all available Army units to head to areas of the country stricken by floods, Wandsworth Council said.
Several train firms said Crewe station was evacuated and all services stopped after the roof was blown off the station. There were also problems with overhead power lines in the area.
London Midland tweeted: "Crewe all services through this station have been stopped due to roof being blown off, debris. I will update as soon as I have more info."
Virgin Trains added: "NEW: Owing to overhead wire problems between Crewe and Liverpool Lime Street all lines are blocked, delays of up to 30 mins are expected."
A man was taken to hospital after becoming trapped under a fallen tree in Chivenor, Barnstaple, Devon.
Two fire crews discovered the man trapped under a large branch of the tree at around 2.15pm today.
Firefighters used small tools and lift equipment to release him.
A spokesman for Devon and Somerset Fire and Rescue Service said: "Crews also used airbags to lift the branch and the male was conveyed to hospital via ambulance."
A spokesman for Cheshire Fire and Rescue Service said firefighters were called to Crewe train station after roof panels fell on to overhead lines and caused a small fire.
A Network Rail spokeswoman confirmed the station had been evacuated as a "precaution" and trains were not stopping there.
The AA said it had attended 29 flood-stricken vehicles today, bringing the total to more than 680 since Friday.
Darron Burness, head of the AA's flood rescue team, said: "We've never seen anything like it. The scale of the flood devastation is sobering and our crews report seeing hundreds of cars submerged in water, often still stuck on the drive.
"At the moment the number one priority is getting our members to safety. The cars are an insurance job - written off.
"However, if your area is still at risk of further flooding, try to move your car to higher ground, if it's safe and practical to do so."