EU nationals living in the UK will be given the right to stay permanently after Brexit and treated like British citizens, Mrs Theresa May told European leaders last night. Any EU citizen in the UK with five years residence at the cut-off date will be granted UK settled status.

Mrs May made a clear commitment that “no EU citizen currently in the UK lawfully will be asked to leave the country at the point that the UK leaves the EU, and all EU citizens lawfully here at the point the UK leaves will have the opportunity to regularise their status to remain in the country.”

She said: “This position represents a fair and serious offer – and one aimed at giving as much certainty as possible to citizens who have settled in the UK, building careers and lives, and contributing so much to our society.”

However, she insisted that it is “vital” that any deal will have to be “reciprocal” arrangement based on the European Union granting the one million British citizens who live in the Europe the same rights.

Theresa May refused to meet EU demands that the “cut-off date”, after which EU citizens will no longer automatically be entitled to stay in the UK, should fall on the day that Britain leaves the European Union. The cut-off date will be decided through negotiation and could fall at any point between March 29 2017, the date that Article 50 was triggered, and the date that Britain leaves the European Union, which is expected to be in March 2019.

All those arriving after the “cut-off date” will be given a two year “grace period” after UK exits from EU and will be subsequently expected to regularise their status by obtaining a work permit or return to their home countries. Once they regularise their status they will be entitled to a special category of “settled status”, conferring the same rights to work, pensions, NHS care and other public services as British citizens, which they will maintain for life.

After the grace period has elapsed, newly arriving EU citizens will be subject to whatever immigration system replaces freedom of movement after Brexit.

Mrs May also refused demands that the European Court of Justice should continue to oversee the rights of EU migrants after Brexit. She said: “The commitment that we make to EU citizens will be enshrined in EU law and enforced through our highly-respected courts”.

The prime minister's proposals were welcomed by her fellow European leaders.  Angela Merkel, the German chancellor, called May’s offer a “good start” but said many other issues related to Britain’s departure from the bloc still need to be resolved.

“Theresa May made clear to us today that EU citizens that have been in Britain for five years will retain their full rights. That is a good start,” Merkel told reporters. “But there are still many other questions linked to the exit, including on finances and the relationship with Ireland. So we have a lot to do until (the next EU summit in) October.”

UK’s Chancellor, Mr Philip Hammond said the government will make the economy the top priority in talks, and could agree to transitional arrangements lasting up to four years, to avoid the country being driven over a “cliff edge” as a result of the talks.