Labour MPs have told Theresa May that a fresh bill on workers’ rights, not just an amendment, would be the minimum they could accept in order to secure their backing for her Brexit deal.

The prime minister met Labour MPs including John Mann, Caroline Flint and Gareth Snell in her House of Commons office on Monday night, where some of the MPs present said an amendment to the trade bill or any other legislation “would not cut the mustard”.

Neither Flint nor Snell backed her deal in the previous vote in early January, though Mann voted with the government.

On Tuesday, May told the House of Commons after the meeting that she was prepared to consider legislating to ensure her commitments on workers’ rights had legal force – though it stopped short of a commitment to a standalone bill.

MPs have said the guarantees should include a “regression lock” to ensure UK standards did not slip below those of the EU as well as opportunities for MPs to vote on raising UK standards when future EU laws are implemented.

Speaking to MPs, May said that was actively being considered. “In the interests of building support across the house, we are also prepared to commit to asking parliament whether it wishes to follow suit whenever the EU changes its standards in these areas,” she said.

MPs are also believed to have urged the prime minister to continue discussions with trade unions, particularly those representing manufacturing industries such as Unite and GMB.

In her statement on Tuesday, May suggested she was preparing to offer other concessions demanded by union leaders, including Unite’s Len McCluskey, on rules governing agency workers.

May said the government had plans to repeal the so-called Swedish derogation, which allows employers to pay their agency workers less. “We are committed to enforcing holiday pay for the most vulnerable workers,” she said. “Not just protecting workers’ rights, but extending them.”

Unions are also understood to have demanded other legal changes from the prime minister in return for their backing, including the right to conduct electronic workplace ballots rather than relying on postal voting.

The business secretary, Greg Clark, told MPs at business questions earlier on Tuesday that he and the GMB general secretary, Tim Roache, had met to discuss those requests.

The Labour leader, Jeremy Corbyn, who has exchanged letters with May over the past week over ways the parties could find common ground, dismissed any suggestion of trusting the Conservatives to legislate to protect workers’ rights.

“For many of them, ripping up rights is what Brexit is all about,” he said, quoting the international trade secretary, Liam Fox, who said: “It is too difficult to hire and fire, and too expensive to take on new employees. It is intellectually unsustainable to believe that workplace rights should remain untouchable.”