Plans to allow the United Kingdom an exemption from EU rules on freedom of movement for up to seven years while retaining access to the single market are being considered in European capitals as part of a potential deal on Brexit.

Senior British and EU sources have confirmed that despite strong initial resistance from French president François Hollande in talks with prime minister Theresa May last week, the idea of an emergency brake on the free movement of people that would go far further than the one David Cameron negotiated before the Brexit referendum is being examined.

If such an agreement were struck, and a strict time limit imposed, diplomats believe it could go a long way towards addressing concerns of the British people over immigration from EU states, while allowing the UK full trade access to the European market.

While the plan will prove highly controversial in many member states, including France, Poland and other central and eastern European nations, the attraction is that it would limit the economic shock to the EU economy from Brexit by keeping the UK in the single market, and lessen the political damage to the European project that would result from complete divorce.

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High-ranking UK officials said that while it was “very early days”, some form of extended emergency brake was “certainly one of the ideas now on the table”.

Any such agreement would, however, mean the UK would still have to pay a substantial contribution into the EU budget, although probably at a lower rate, and would lose its seat at the negotiating table when rules on the single market were determined, because it would not be a full member of the union.

During the referendum campaign, the leave camp, led by Boris Johnson, now the foreign secretary, and Michael Gove, suggested that the UK would save £350m a week in EU contributions as a result of leaving both the EU and the single market. They said the money could be spent on the National Health Service.

But on a visit to the United Nations in New York this weekend, Johnson appeared to change his tune, suggesting he now believed a deal could be struck that would allow the UK access to the single market with new limits on free movement rules for European workers.

“I’ve absolutely no doubt that that balance can be struck, and over the next few weeks we’ll be discussing that in the government and with our European friends and partners,” Johnson said.

“Everybody wishes to make fast progress in the economic interests both of Britain and of the European Union. I think there is very much a deal there to be done, and the faster we can get it done the better.”

If the rights of EU citizens now in the UK can be guaranteed, then I think we can look at some form of emergency brake Dutch MEP Hans van Baalen

EU diplomats and advisers believe the EU should try to keep the UK in the single market if possible, while not giving it such a good deal that other member states would be tempted to follow it out of the club.

Speaking in her capacity as deputy director of the Rome-based Institute for International Affairs, Nathalie Tocci, who is a special adviser to Federica Mogherini, the EU high representative for foreign and security policy, said she believed that the Italian government would back an emergency brake as a way to keep the UK in the single market.

She added that it would have to be time limited, in order not to violate EU treaties. “But I see no reason why it could not last, say, between seven and 10 years. This was how long temporary derogations lasted after the 2004 enlargement, which the UK chose not to benefit from,” she said.

The Dutch MEP Hans van Baalen, who is president of the Alliance of Liberals and Democrats for Europe party and a member of the same party as the Dutch prime minster, Mark Rutte, said the plan should be taken forward, but would require the UK to give firm assurances about the right of EU citizens currently living and working in Britain to remain in the country.

“If the rights of EU citizens now living the UK can be guaranteed permanently by the UK government, then I think we can look at some form of emergency brake on free movement of labour,” he said. “This could be invoked when the British labour market is under particular pressure. I would try to limit it to the UK at this stage.

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“It is difficult to talk in too much detail as this will take a long time to negotiate. But given the difficulties we face, we must try to be flexible. It is vital that we have the UK in the single market as much as possible for the UK economy and for the economies of all EU member states.”

In his attempt to renegotiate the terms of the UK’s EU membership before the referendum, Cameron secured a limited emergency brake that would have enabled Britain to restrict and phase in EU migrants’ access to in-work benefits for the four years after they first arrived in this country.

The UK would be able to apply the “brake” for an initial seven years. But after the Brexit vote the EU declared the deal null and void.

Under current European Economic Area rules (which cover EU member states as well as non-EU members like Norway, which has full access to the single market) there is already an option to apply “safeguard measures” in the event of “serious economic, societal or environmental difficulties of a sectorial or regional nature liable to persist”.

This would allow Norway to impose restrictions on free movement but it has never invoked the clause, because, diplomats say, it is wary of reprisals from EU member states.