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The UK will not be allowed to remain in the European single market if it does not wish to keep the freedom of movement rules, European Union leaders have warned.

With immigration a key part of the Leave campaign in the EU referendum, many Leave voters are expecting the UK to ditch freedom of movement. But Brexiters are adamant a deal to remain in the single market will be struck.

Jean-Claude Juncker, president of the European Commission, said that any country wanting to be part of the single market must adopt freedom of movement laws.

With David Cameron saying Article 50 - the legal process of leaving the European Union - would not be triggered until a new Prime Minister is in place, Mr Juncker stressed that there would be "no negotiation without notification". Some have suggested that the UK should and could start informal negotiations over its withdrawal before Article 50 is invoked.

On Tuesday, Mr Cameron said immigration levels were a "great concern" of the public, and conceded that it would be a "huge challenge" to gain access to the single market and lose the freedom of movement rules once the UK leaves the EU.

Hollande's plan

Now that the UK has voted to leave the EU, the country's ideal solution is to secure what it being referred to as an 'EEA+' agreement. That would see the UK remain in the European Economic Area (EEA), keep passporting and gain control over its borders.

But, Mr Juncker, German Chancellor Angela Merkel and French President Francois Hollande, have already dismissed that possibility.

Passporting, if you are not familiar, allows UK banks to to business with the rest of the EU. Without it, the City of London and the UK's financial services industry would crumble.

Germany and Brussels are in favour of a so-called 'EEA-' agreement. That would give the UK access to the single market, but remove passporting and maintain freedom of movement rules.

According to journalist and author Ben Judah, Francois Hollande plans to be a lot more measured and cynical in his approach to negotiations. Judah believes that Hollande wants a slightly different 'EEA-' deal, which would include access to the single market, the removal of freedom of movement laws, and the removal of passporting.

As Judah explains, Hollande would basically be saying "you get less Poles, but we want your banks". It leaves the next Prime Minister in a dire situation. In basic terms, the deal favoured by Hollande is what the British public wants. It wants to remain part of the single market, and it wants to reduce immigration. For the large part, the public does not know about passporting.

The next Prime Minister, whoever it may be, would be forced to choose between pleasing the public and seriously damaging the economy, or angering around half of voters and keeping the bankers (and the Treasury happy). The loss of passporting would likely see most, if not all, banks headquartered in London cross the channel to Paris. HSBC has already announced it is moving 1,000 jobs to Paris following the Brexit vote.

The banking sector contributes enormously to the UK economy, in excess of £31 billion a year according to PwC. Losing that amount of money from the government tax income would be catastrophic.

Speaking at the end of a summit on Tuesday, President Hollande said: “The City, which thanks to the EU, was able to handle clearing operations for the eurozone, will not be able to do them.

“It can serve as an example for those who seek the end of Europe . . . It can serve as a lesson.”