Prime Minister Theresa May is set to tell parliament on Monday (local time) that 95 per cent of Britain's divorce deal has now been settled, amid reports that she could face a no-confidence motion as early as this week.

Key points: The Mail on Sunday quoted Conservatives saying Ms May is in a "last chance saloon"

The Mail on Sunday quoted Conservatives saying Ms May is in a "last chance saloon" Ms May will restate that she will not accept a hard border with Northern Ireland

Ms May will restate that she will not accept a hard border with Northern Ireland 48 Conservative Party backbenchers are needed to trigger the no-confidence motion

Facing some of the fiercest criticism to date over her Brexit plans after the two sides failed again to reach agreement at a summit last week, Ms May will try to calm passions in parliament where her strategy has angered Eurosceptics and EU supporters alike.

With just over five months until Britain leaves the EU, talks have stalled over a disagreement on the so-called Northern Irish backstop, an insurance policy to ensure there will be no return to a hard border on the island of Ireland if a future trading relationship is not agreed in time.

But Ms May's attempt to unlock the talks by considering an extension to a status quo transition period beyond the current proposed end date of December 2021 has further stirred passions at home.

In an attempt to highlight how much progress has been made in more than a year of talks with the EU, she will tell parliament the government has reached agreement on everything from Gibraltar to future security over the last three weeks.

"Taking all of this together, 95 per cent of the Withdrawal Agreement and its protocols are now settled," she will say, according to excerpts from her statement to parliament.

"The shape of the deal across the vast majority of the Withdrawal Agreement is now clear."

Ms May's speech will come on the back of reports that members of her own Conservatives Party were planning a vote of no confidence as early as this week.

The Mail on Sunday reported politicians from Ms May's Conservatives said she was in the "last chance saloon" and should "bring her own noose" when she addresses Conservative MPs at a party meeting in parliament on Wednesday.

A vote of no confidence for Ms May would be triggered if 48 Conservative MPs submit letters to the chairman of the party's so-called "1922 committee" of backbenchers demanding such a vote.

The Sunday Times said 46 had now been sent.

"We are at the end stage of the negotiation. I think it is understandable there are jitters on all sides of this debate, we need to hold our nerve, the end is in sight in terms of a good deal ... I think colleagues should wait and see what that looks like," said Brexit Minister Dominic Raab.

"Now is the time to play for the team."

Protesters at the People's March in London called for another vote on Brexit. ( Reuters: Simon Dawson )

In her speech, Ms May will also repeat her opposition to the EU proposal for Northern Ireland to remain in the bloc's customs union, potentially creating barriers to trade with the rest of Britain — she is attempting to ease growing frustration among her parliamentary partners, a Northern Irish party.

"As I set out last week, the original backstop proposal from the EU was one we could not accept, as it would mean creating a customs border down the Irish Sea and breaking up the integrity of the UK," she will say.

"I do not believe that any UK Prime Minister could ever accept this. And I certainly will not."

But the withdrawal agreement, or the terms of Britain's divorce, cannot be signed off until the two sides agree on the Northern Irish backstop.

At an EU summit last week, any such agreement seemed just as far off as it did months earlier, with EU officials and diplomats saying Ms May had offered nothing new to unlock the talks.

Since then, MS May's proposal to extend the transition period has done little to calm anger among Eurosceptics in the governing Conservative Party, who fear she is leading Britain into a deal that will make Britain a "vassal state" — unable ever to leave the EU.

Sorry, this video has expired Anti-Brexit protesters march through London

ABC/Wires