THE Scottish Government is in private talks with Gibraltar about a radical plan to keep parts of the UK in the European Union despite last week’s Brexit vote.

The talks could also involve the government of Northern Ireland, which, like Scotland and the overseas territory, voted to Remain.

READ MORE: Nicola Sturgeon not seeking 'green light' for another independence referendum in emergency debate

In the coming days, Nicola Sturgeon is to embark on a diplomatic offensive in which she will lobby Brussels and EU member states to “explore all the possible options” about Scotland staying in the EU.

Fabian Picardo, Gibraltar’s chief minister, has confirmed talks have already begun with the First Minister. He told BBC Newsnight: "I can imagine a situation where some parts of what is today the member state United Kingdom are stripped out and others remain.

READ MORE: Nicola Sturgeon not seeking 'green light' for another independence referendum in emergency debate

"That means that we don't have to apply again for access[to the single market], we simply remain with the access we have today, and those parts that leave are then given a different sort of access, which is negotiated but not necessarily under Article 50," he explained, referring to the provision in the Lisbon Treaty, which sets out how a member state can voluntarily leave the EU.

However, during a Commons statement on the referendum result, David Cameron was asked to give an assurance that it would not be possible for “devolved institutions to wield a veto” on the Brexit process and replied that this was “principally, a matter for this Westminster, United Kingdom Parliament”.

READ MORE: Nicola Sturgeon not seeking 'green light' for another independence referendum in emergency debate

Earlier, his spokeswoman was asked about whether or not the Scottish Parliament had the ability to veto Brexit and replied: “Foreign policy is a reserved matter and this was a decision taken by the United Kingdom.”

Downing Street also sought to pour cold water on the prospect of a second Scottish independence referendum by declaring: “The last thing that Scotland needs now is a divisive referendum.”

The spokeswoman insisted the reasons for Scotland to remain in the UK were as strong now as they were 18 months ago, adding: “What we all need to do is to focus on getting the best deal for Scotland and the UK in these negotiations.”

But Fergus Ewing, the Scottish government’s farming minister, claimed to have received a "sympathetic hearing" from his European counterparts over Scotland's bid to remain in the EU, noting how senior EU officials had told him they would like to see Scotland as the bloc’s new 28th member state.

In his statement to MPs, the Prime Minister stressed how it was imperative the interests of all parts of the UK were “protected and advanced” in the Brexit talks, which meant that the devolved administrations would be “fully involved”.

Announcing the creation of a Brexit Unit in Whitehall, bringing together top civil servants to advise ministers on the complex collection of issues ahead, Mr Cameron added: “Our officials will be working intensively together over the coming weeks to bring our devolved administrations into the process for determining the decisions that need to be taken.”

Meantime, the PM and his chancellor moved to calm nerves over Britain's withdrawal from the EU as the financial markets responded with continued volatility.

Both Mr Cameron and George Osborne acknowledged the coming months would not be "plain sailing" and made clear they expected "adjustments" to the expected path of the economy but insisted the UK was strong enough to weather the storm.

However, their efforts were not enough to prevent another day of turbulence on the markets with the pound dropping to a 31-year low against the US dollar while more than £40 billion was wiped off the value of Britain's biggest companies as the FTSE 100 Index fell 2.6 per cent.

Such was the market volatility at one point that some shares had to be temporarily suspended as the losses stack up. Royal Bank of Scotland, 73 per cent owned by the taxpayer, briefly plunged to its lowest level since 2009 before finishing more than 15 per cent down at 174.3p.

After the chancellor made clear an emergency post-Brexit budget was now unlikely until a new prime minister was in place in the autumn, Boris Johnson, tipped by many as the lead contender to succeed Mr Cameron, declared: "Project Fear is over."

In response, Ms Sturgeon tweeted: “Indeed, Boris. Project Farce has now begun – and you are largely responsible.”

The UK suffered a further blow as US ratings agency Standard & Poor's stripped it of the top credit grade following a similar move by Moody's on Saturday.

On a day of high political drama at Westminster, the Labour Party was plunged into turmoil as more than 30 shadow ministers resigned their frontbench posts, making clear they did not think Jeremy Corbyn was up to being leader and prime minister.

At a stormy meeting of the parliamentary Labour party, the leader was told to “do the decent thing” and step down. Afterwards, many MPs appeared close to tears. Former leadership contender Chuka Umunna described the event as "pretty catastrophic".

Later at a pro-Corbyn rally outside the Commons, the Labour leader called for "unity," telling thousands of supporters: “Don't let the people who wish us ill divide us."

Elsewhere, it was suggested Stephen Crabb, the Scots-born Work and Pensions Secretary, and Sajid Javid, the Business Secretary, were poised to stand on a joint ticket for the Tory leadership.

The 1922 Conservative backbench executive has drawn up plans for a contest that could see the new leader and, thus, prime minister, in place by September 2; a month earlier than expected. Nominations are due to open Wednesday evening and close Thursday afternoon.

Leading Brexiter Boris Johnson, regarded by many as the favourite, and his Remain colleague Theresa May, the home secretary, have been taking soundings with colleagues and are both expected to declare their candidacies shortly.

In a separate development, Jacques Gounon, head of Eurotunnel, warned that the Brexit vote could lead to a summer surge in illegal migrants trying to enter Britain from France before new restrictions are enforced.

“I'm afraid that we could have an increased migrant pressure during this summer, as a Brexit consequence," he said.