Home secretary says she wants to guarantee positions of EU citizens already in UK and those of Brits abroad

Theresa May has said there could be an upsurge in the number of Europeans moving to the UK before Britain’s exit from the EU, as people try to enter the country ahead of any new immigration controls.

The home secretary, who is the frontrunner in the race to succeed David Cameron as prime minister, said the rights of EU citizens already living in the UK, and those of Brits abroad, would have to be dealt with as part of any Brexit negotiations, but she said she hoped they would be secure.

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“We are still members of the EU – there is no change in their position currently. But of course as part of the negotiation we will need to look at this question of people who are here in the UK from the EU,” she told ITV’s Peston on Sunday. “I want to ensure that we are able to not just guarantee the positions of those people but guarantee the positions of British citizens in other member states.”

It comes after Nicola Sturgeon, Scotland’s first minister, wrote to Cameron and the five Tory leadership candidates to say it was imperative to respect the rights of 173,000 EU citizens in Scotland. She called for “immediate guarantees”.

Meanwhile a letter signed by prominent figures in both the remain and leave campaigns, including the chair of Vote Leave, Gisela Stuart, warned of “considerable anxiety for the 3 million EU citizens who have made their homes in the UK, and the 1.2 million British citizens living in other EU countries”. Writing in the Sunday Telegraph they call on the candidates to offer an “unequivocal statement” that EU migrants in the UK are welcome and that any changes will only apply to new migrants.

But while May appeared to suggest she would seek guarantees, she will also have to deal with the question of the point at which new rules are enacted, and whether they could be set retrospectively to avoid incentivising a spike in immigration.

May said she had discovered over six years as home secretary that it was difficult to set in place a time period during which net migration could be brought down. So far the Tory government’s promise to reduce it to the tens of thousands has been repeatedly missed as figures go in the opposite direction.

“If we are looking ahead – we might see in the run-up to [an EU deal] people wanting to come to the UK before that exit happens – so there are factors you can’t always predict,” she said.

May said she did not want to offer an early general election because she had stood on the mandate won in 2015, but also because it would be a “destabilising factor” during an uncertain time. She denied she wanted to see other Tory leadership candidates stand aside to effectively allow a coronation in the name of stability, saying instead she felt it was right for party members to vote on two candidates.

Responding to the suggestion, by her opponents Andrea Leadsom and Michael Gove, that a Brexit-supporting minister should take over the government, she pointed out that 17 million people had voted to leave and 16 million to remain. May said: “I’ve been clear that Brexit means Brexit – now we have to bring those sides together. The question is not what was your view 10 days ago, [but] what are you going to do now?”