Appearing before MPs to meet a requirement set by parliament following the 230-vote defeat of her proposed Brexit deal, Mrs May announced that European Union citizens would no longer need to pay £65 to apply for settled status, allowing them to live and work in the United Kingdom beyond 2020.
The prime minister will address the Commons on Monday afternoon, setting out how she intends to proceed with the Brexit withdrawal agreement.
Jeremy Corbyn is likely to refrain from making fresh moves towards backing a second referendum until after the government's Brexit plan B is voted on later this month, as he seeks to balance pressure from rival wings of his party.
He said: "Our amendment will allow MPs to vote on options to end this Brexit deadlock and prevent the chaos of a no deal".
Germany and France are among countries that have taken national steps to make sure that financial contracts concluded with firms in the United Kingdom can be serviced even if the United Kingdom leaves without a deal on March 29.
The Commons is roughly split into four groups: the no deal zealouts, supporters of May's deal, backers of a Norway-style Brexit and the second referendum crowd.
But a series of non-binding free votes - Edward Heath gave Tory MPs such freedom in 1971 when Britain was preparing to join the EEC - would, at the very least, show where the balance of power actually rests in Parliament.
Labour's Hilary Benn has tabled an amendment to the Government motion calling for a range of indicative votes on various Brexit options.
The order will apply for a year and will take effect from 10 February. If the prime minister will not move her red lines she can see what is going to happen and that is parliament taking control of the process.
The Great Grimsby MP tweeted: "This may mean that I am required to step down from my front bench housing role if it is a whipped vote".
Keir Starmer, the shadow Brexit secretary, appeared keen to push Labour's policy in that direction in a carefully worded speech on Saturday, and some shadow cabinet colleagues believe he is positioning himself as the champion of a people's vote.
Presenting her "Plan B" to the Commons on Monday, Mrs May said she would conduct further talks on the controversial Irish border backstop proposals, and promised to give Parliament "a proper say" in negotiations on the future relationship between the United Kingdom and EU.
"There is a clear majority in the House to support a deal and to respect the referendum result", he says, but he says the PM needs to work across the House.
A humbled Theresa May offered MPs and devolved administrations a bigger role in Brexit and scrapped fees for European Union citizens applying to stay in the United Kingdom as she battles to save her deal with Brussels.