David Davis says some people who arrive before UK leaves EU may not be given leave to stay indefinitely

The government could set a retrospective cut-off date for permitting overseas EU nationals to remain in the UK after the country leaves the union, the minister responsible for the negotiations, David Davis has warned.

Appointed last week to the new role of secretary of state for exiting the European Union, Davis said it might not be possible to warn in advance when this date might fall, as the “sheer generosity” of rights granted to EU nationals could prompt a surge in new arrivals.

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“One way of dealing with it could be saying: ‘OK, only people who arrived before a certain date get this protection,’” he told Sky News’s Murnaghan show on Sunday. “There are other ways too.”

Davis, a long-time Eurosceptic who had been off the Conservative frontbench since 2008 – when he stepped down as shadow home secretary in a protest over civil liberties – said being too specific in advance could cause difficulties. “If you set a date, that’s when you start the rush,” he said.

Theresa May was the only one of the Conservative leadership candidates to say she would not pre-emptively guarantee the rights even of foreign EU nationals already living in Britain before the referendum.

It brought complaints from opponents, notably the shadow home secretary, Andy Burnham, that she was using EU nationals in the UK as “bargaining chips”. A Labour motion calling for rights to be guaranteed passed the Commons earlier this month, but is not binding.

Facebook Twitter Pinterest As well as Davis, May appointed Brexit supporters Boris Johnson and Liam Fox to her cabinet. Composite: Daniel Leal-Olivas/PA/AFP/Getty Images/Reuters

Davis said on Sunday that any deals on people in the UK must be done at the same time as arrangements about the 1.2 million Britons living elsewhere in the EU, as it would stop “anybody being used as bargaining counters”.

It was important not to make any early promises to people living in the UK, Davis said. “If we make a very generous settlement, as I’d like to do, then people are going to say: ‘Oh but then that’ll attract lots more people in because they want to beat the deadline.’

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“And so what I’ve said is, let’s deal with that issue when we come to it. One way of dealing with it could be saying: ‘OK, only people who arrived before a certain date get this protection’ – there are other ways too. But we’ve got to do it within the law as it stands because at that point we’ll still be within the European Union.

“Bear in mind this is only an issue if there is a surge in people arriving, and I don’t think that is by any means certain.”

Davis dismissed the idea that speaking even hypothetically about a cut-off date for residency rights could spark a movement of people to the UK. “No it won’t be like that,” he said. “If you set a date, that’s when you start the rush.”

There was no new Labour response to Davis’s comments, but the SNP described them as shameful and indicative of a “nasty party cabinet” under May.

Davis accepted that a cabinet headed by May, who campaigned for the UK to remain in the EU, and including prominent Brexit supporters such as him, Boris Johnson and Liam Fox, meant there would be tensions over the exit strategy.

Davis suggested the UK could trigger article 50, which would begin the formal two-year process of leaving the EU, “early next year”. May has indicated a longer process, saying she hopes to create more national consensus on a post-Brexit future first.

In another issue likely to dominate his new role, Davis said Scotland would not be able to unilaterally halt Brexit, and dismissed the proposal by Scotland’s first minister, Nicola Sturgeon, that her nation could remain in the EU even as the rest of the UK leaves.

“I don’t think that works,” Davis said. “One of our really challenging issues to deal with will be the internal border we have with southern Ireland, and we are not going to go about creating other internal borders inside the United Kingdom.”

He added: “The aim here is to try to address the concerns of people who are basically remain people, who say: ‘Well, we are worried about inward investment, we are worried about trade with Europe, we are worried about all sorts of things.’

“And we will try as best we can – they can’t have a veto because there are 17.5 million people who have given us a mandate, they have told us what to do, we can’t disobey it – but what we can do is to try to do what we can to minimise any disruption or turbulence or problems.”