The UK's drivers throw away billions of pounds a year by accepting their existing motor insurer's quote at renewal time.

Many assume they already have the best possible deal, or that switching will be a lot of effort for little gain, but shopping around can produce valuable savings.

September, October, March and April are the busiest months for renewals, as new registrations trigger a spate of car purchases.

But too many drivers miss the opportunity to cut their premiums. Price comparison website Gocompare.com says they could be wasting up to £4.7 billion annually by allowing their policies to auto-renew.

It calculates that 44% of motorists haven't switched provider for more than two years. Each could be overpaying by hundreds of pounds.

Scott Kelly, the site's head of motor insurance, says: "Different insurers assess risks differently.

"We know from our own figures that motorists can save an average of £399.50 by simply changing their insurer. Yet, incredibly, just under a third of drivers haven't switched for more than three years and, during this period, the average fully comprehensive car insurance premium has more than doubled."

According to the AA's British Insurance Premium Index, the typical cost of comprehensive cover was £751 at the start of 2009. By this year it had risen to £1542.

Many of those who stay put can't be bothered to seek a better deal. Others think the provider who offered them the lowest price in the past will still be cheapest. But Kelly points out: "In the last couple of years all insurers have been forced to revise their rates, so drivers shouldn't take anything for granted."

Despite the overall trend upwards, the AA says the motor market is currently in turmoil, with some providers actually cutting prices.

The AA's Simon Douglas explains: "Competitive pressure is leading some companies to make big premium cuts on price-comparison sites so that they can increase their portfolio of customers."

Several providers, including Aviva and Direct Line, advertise the fact that they don't do business through these sites and suggest this actually makes them more competitive.

For some, they will offer the lowest price, but it is by no means certain. The only way to be sure you are getting the best deal is to get quotes from a range of providers – and the quickest and easiest way to do that is by using a comparison site.

It should take about 20 minutes to input your details and get a selection of prices, but since sites don't all list the same providers, it is wise to check two or three. Even if it takes you an hour, it could be well worth the time and effort.

Don't choose a policy without checking the cover meets your needs. If it doesn't pay when something goes wrong it is worse than useless.

You could reduce your premium considerably by increasing the voluntary excess or opting for third party, fire and theft cover instead of fully comprehensive, but if you have an accident and have to foot a large bill, you could regret it.

Other less painful ways to cut the cost of car insurance include:

l Building up a no-claims bonus.

l Parking overnight in a garage or private driveway, rather than the road.

l Fitting an approved security device.

l Adding an older named driver with a good track record.

l Reducing the number of miles you drive.

You can also save around 10% with many insurers by paying for the whole year up front rather than opting for monthly instalments, as these generally include an element of interest on the outstanding sum.

Two of the easiest ways to cut car-cover costs are not to make modifications and not to speed. Fitting accessories could add up to two-thirds to your premium, according to Moneysupermarket.com.

The comparison site says a man aged 30 putting alloy wheels on his Ford Fiesta might increase the annual insurance cost by 30%, while a complete new body kit could lead to a 66% rise.

Pete Harrison, Moneysupermarket's car insurance expert, warns: "It pays to contact your insurer before you go ahead and make any modifications, as you will need to decide whether the extra cost to cover the changes is worth paying. Some insurers won't offer insurance to cars that have already been modified, so it's crucial to check with your provider - drivers need to realise that not informing an insurer of modifications made to a vehicle can invalidate a policy."

If you get caught speeding you won't just get a fine and points on your licence. Your premium will rocket too, and serial speeders can find it hard to get insurance cover at any price.

Moneysupermarket calculates the average 30-year-old man with three points on his licence would pay £439 for a year's cover, while six points might boost this to £702.

Harrison adds: "Not only are motorists who flout the law by speeding risking the lives of other road users and pedestrians as well as their own, but for repeat offenders, they run the risk of insurers refusing to provide them with cover."