Theresa May has promised that 3.2million EU nationals living in the UK will be allowed to stay
Any migrants who arrive in the UK before March 2019 will be entitled to stay without restrictions.
UK officials also believe they have persuaded Brussels that EU citizens will not have the right to bring spouses and other relatives to the UK after Brexit.
In a letter to EU citizens, Theresa May said: “When we started this process, some accused us of treating EU nationals as bargaining chips. Nothing could have been further from the truth.
“EU citizens who have made their lives in the UK have made a huge contribution to our country. And we want them and their families to stay.
“I couldn’t be clearer: EU citizens living lawfully in the UK today will be able to stay.”
The PM pledges to allow EU citizens to stay in the UK after Brexit with or without a deal.
If there is a deal she will give them a say on the registration process by setting up “user groups” and she will scrap the current EU rules for them to have Comprehensive Sickness insurance to live in the UK.
EU citizens will be subject to a minimum income test.
This is currently required for all British citizens who to bring family members from outside the EU to the UK.
It comes as ministers are becoming concerned that the EU is deliberately stalling negotiations in a bid to extract a bigger Brexit divorce bill from the UK.
President of the European Parliament Antonio Tajani claimed that Mrs May’s offer of £18billion is “peanuts”.
The offer comes as Eurosceptics today demanded that the PM abandons the Brexit negotiations if the EU again refuses to budge.
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Brexit Secretary David Davis said this week: “The simple truth is that we are in a negotiation and they are using time pressure to see whether they can get more money out of us – that is what is going on, as is obvious to anybody.
“That will take some time, but I am sure we will get there in time to get a decent outcome for everybody.”
The EU chief negotiator Michel Barnier proposed an outline of a final deal on citizen’s rights at the EU’s Brexit working group on October 5, but it was rejected.
A source who briefed on the meeting told the Telegraph: “Barnier put forward the outlines of a UK compromise on citizens’ rights, but the consensus was that it was too early to settle on the citizen’s file.
David Davis said the EU is trying to delay talks
“The fear was that if the EU settled the citizens’ rights file, it would open the EU to suggestions from the British side that the EU was being unfairly intransigent on the money side. The decision was taken to stall.”
It comes following concessions by the Prime Minister last month in Florence in a bid to get talks moving.
Mrs May also conceded that Article 50 should be written directly into UK law, which was previously dismissed as “unnecessary”.
The PM also said the UK would “take into account” EU court judgements about EU citizens’ rights after Brexit.
Antonio Tajani said that the UK’s offer of £18 billion is “peanuts”
Mrs May will also mount an appeal with all 27 EU leaders to ease businesses’ exit fears by starting talks about a two-year transition.
EU Council President Donald Tusk declared last night he recommending that “the EU27 to begin internal preparations for talks on the transition and the future relationship”.
He insists that the progress has been “promising” but not sufficient to begin trade talks.
A leaked German Government paper revealed Berlin wants to offer the UK a “comprehensive free-trade accord”.
Hungary also warned that a failure to agree on a trade deal with the UK will have “tragic consequences for the European economy.”
Foreign Affairs minister Péter Szijjártó said the UK “provides one-seventh of the EU’s economic performance”.