On the first day of votes that could further complicate her tortured negotiations to quit the European Union, parliament will debate a demand for a "meaningful vote" on any agreement May negotiates with Brussels before leaving the bloc next March.
She could be heard being cheered from outside the room in parliament where lawmakers from both sides of the debate, including some of her ministers, gathered on the eve of the votes. This would have thereby given parliament more power to set the government's direction if the agreement is rejected.
If it had been accepted the amendment would have given the lower chamber, the House of Commons, a "meaningful vote" on any deal agreed with Brussels before Britain leaves the European Union in March next year.
He added: "I understand the difficulties MPs representing constituencies which voted strongly for Leave or Remain have on the EEA amendment".
Ukip leader Gerard Batten said: "The only "meaningful vote" was the verdict of the people in referendum of June 23 2016".
After days of frantic lobbying by Conservative officials to try to get the party on board, May renewed appeals for unity over the "meaningful vote", after the government appeared to have secured a compromise to stop a similar rebellion on Wednesday over Britain's trading ties with the EU.
The government fears a weakened negotiating position.
The Labour leadership this month drafted its own amendment to replace the Lords' one on the EEA, demanding a vote on negotiating a new single market deal with the bloc.
To avoid defeat, the government promised to make its own changes to the bill to strengthen Parliament's powers.
Former Conservative Attorney General Dominic Grieve has led the charge on keeping the Charter on the statute books after Brexit.
An agreement that defused a potential rebellion over handing parliament more control over Britain's exit from the European Union looked in danger of unravelling on Wednesday, when the two camps argued over the shape of a possible compromise on a "meaningful vote".
The parts of his amendment which he expects to be taken forward by ministers provide a mechanism by which Parliament has to be consulted by the end of November in the event of no deal or if a proposed agreement is rejected, he said.
Chuka Umunna, a pro-EU colleague, told lawmakers that opposition to immigration should be met "in a Labour way" - as it was when some of the party's working-class base objected to immigrants from the Caribbean and Africa in the 1960s.
Asked whether he backed calls for a so-called "People's Vote" on the final Brexit deal, the economist replied: "We've had vote after vote there's no doubt about what the will of the people is on this question".
The "meaningful vote" will be the first major test after the House of Lords introduced 15 changes to the bill, trying to reshape the government's approach to Brexit by encouraging lawmakers to press for the closest possible ties.
He also warned that Britain "would not be ready in time" for Brexit and called for a referendum on the terms of the final deal.
It has also intensified pressure on a prime minister who lost her party's parliamentary majority at an ill-judged election past year and tested her already weakened authority.
In fact, her party is far from united over the decision to leave the EU.
"Now it's Labour's turn to show its dysfunction", said one Labour lawmaker.
Under the proposal, already approved by the House of Lords, Parliament would also seize control of the negotiations if the clock runs out and no deal is reached by March 29 2019 - the day of Brexit.