British Prime Minister Theresa May was set to face a new showdown yesterday with pro-EU MPs over parliament's role in the final Brexit deal, which could influence her entire negotiating strategy.

After months of debate, MPs will vote on the last contested amendments to the EU (Withdrawal) Bill which set out how much power lawmakers will have if the government fails to agree a departure deal before Brexit in March 2019.

May says she expects to get an agreement, but warned that any attempt to tie her hands could weaken her negotiating position with Brussels.

She averted a rebellion by pro-EU MPs in her Conservative party last week with a promise of a compromise on parliament's powers, but within days they had rejected her proposal as inadequate.

The MPs instead worked with peers to introduce their own amendment to the unelected upper House of Lords, which agreed by a landslide on Monday, sending it back to the lower House of Commons.

The main opposition Labour party is backing the amendment but it has its own rebels who could vote with the government.

"The vote will be tight," a government source told AFP.

May's spokesman said Tuesday the government could not accept the proposal, which "would undermine our ability in the negotiations to get the best deal for the country".

He added: "We hope that all MPs will be able to support the government's position."

Phillip Lee, a Conservative MP who resigned as a junior minister last week to vote against the government, said yesterday's vote could go either way.

He said the government continued to try to persuade MPs, telling the BBC: "We were always going to get the normal dark arts of Westminster taking place.

"But my understanding is that the position taken by a number of colleagues is solid, which is why the government is still in negotiations."