About three million EU citizens living in the UK would be allowed to stay after Brexit, Theresa May has proposed.

Under the PM’s plans a new “settled UK” immigration status would grant EU migrants who had lived in the UK for five years rights to stay and access health, education and other benefits.

Proposals were unveiled at a Brussels summit but are dependent on EU states guaranteeing Britons the same rights.

The PM said she did not want anyone to have to leave or families to split up.

“No one will face a cliff edge,” she said.

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“The UK’s position represents a fair and serious offer, 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.”

Many EU citizens in the UK, and Britons living abroad, are worried about their status once Brexit happens. The UK’s exit deadline is 30 March 2019. Some even fear deportation if their EU rights are not guaranteed.

Arriving at the summit, Mrs May said the UK wanted to protect the rights of EU citizens in the UK – and the rights of UK expats in other European countries.

But Downing Street has not yet specified what “cut off” date will be for new residents, after which the guarantee would no longer apply. It will be no earlier than March 2017, when the UK formally began leaving the EU by issuing the Article 50 notification, and no later than March 2019 when it will actually leave.

Those arriving up until the point of departure would have a “grace period” – expected to be two years – to build up the same “UK settled status”, she told EU leaders.

BBC political editor Laura Kuenssberg said the PM was already on a collision course with her European counterparts over her plan for the rules of the new system to be applied by a British court – Brussels has insisted it must be the European Court of Justice that oversees it.

But she added that the offer was intended to be a symbol that the UK was getting on with Brexit at a time of turmoil at home, in the wake of the general election result which led to Mrs May losing her Commons majority.

Not clear

Our correspondent said the full details would not be unveiled until next Monday, and it was not yet clear if the offer was as generous as that put forward by the EU a month ago. Details on issues such as the rights of EU citizens’ relatives abroad and their descendants, were not yet known.

At the summit on Thursday, German Chancellor Angela Merkel told reporters she wanted “the widest possible security guarantees for EU citizens” from the Brexit deal.

Both the UK and the rest of the EU say they want to come to an arrangement to secure the status of about 3.2 million EU nationals living in the UK, and 900,000 Britons overseas.

UK opposition parties had urged the government to make a unilateral guarantee to the EU migrants – but ministers have insisted a reciprocal deal is needed to ensure British expats are protected.