Updating the Commons on how she plans to proceed after her Brexit deal was comprehensively rejected by MPs last week, Ms May said she had heard “powerful representations about the anxieties facing EU citizens in the UK and UK citizens in the EU who are waiting to have their status confirmed”.

She said: “We have already committed to ensuring that EU citizens in the UK will be able to stay, and to continue to access in-country benefits and services on broadly the same terms as now, in both a deal and a no-deal scenario.

“Indeed, the next phase of testing of the scheme for EU nationals to confirm their status has launched today.

“And having listened to concerns from members and organisations like the The3Million group, I can confirm today that when we roll out the scheme in full on 30 March, the government will waive the application fee so that there is no financial barrier for any EU nationals who wish to stay.”

Anyone applying during the pilot phase of the scheme, which runs from 21 January to 30 March, will have their fee reimbursed, she added.

While MPs from all parties welcomed the U-turn, some said the fee should not have been introduced in the first place.

Labour’s Stella Creasy said: “Extraordinary [that] the Tories are now boasting they are scrapping pay to stay for EU citizens.

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“It was their idea in the first place. It’s like the burglar who ransacks your house and then wants a reward for returning something of sentimental value.”

Dave Prentis, general secretary of the Unison trade union, said: “This was the right thing to do. But it’s an idea that should never have seen the light of day in the first place. It’s a pity it took the government so long to see sense.

“With all the talk of a no-deal Brexit, EU nationals have more than enough on their minds, without having to worry about coming up with the cash just so they can carry on living here.

“The settled status registration process must be simple and make European workers feel welcome. The UK simply cannot afford to lose valuable staff from its already strained health and social care sectors.”

EU leaders also welcomed the move. Guy Verhofstadt, the European parliament’s Brexit coordinator, said: “I am delighted the planned settled status fees have been waived. This is a victory for common sense. Throughout the negotiations, the European parliament has pushed to ensure that EU citizens are not financially punished for the Brexit referendum outcome.”