A CONSERVATIVE MP has said he could vote to bring down Theresa May in a no-confidence motion in the House of Commons.

There are reports that Labour leader Jeremy Corbyn is considering a fresh vote against May's government.

A previous bid to oust her in January saw her survive by a majority of 19, with 325 votes to 306.

However, Tory MP Steve Baker said the option of backing a no-confidence vote in his own party's government was "on the table" if May backed a softer Brexit.

Baker has thus far refused to vote in favour of the Prime Minister's deal.

Appearing on the BBC's Politics Live, he had the following exchange with presenter Jo Coburn:

Coburn: "If Theresa May bolts on a customs union, would you vote against her government in a no-confidence motion?"

Baker: "I'm hoping not to reach that point. As a Conservative member of Parliament I would expect always to vote with the government in a confidence motion."

Coburn: "But you said you'd be shattered, that the party would be shattered. If in the end she does what you absolutely vehemently oppose, would you, at that 11th hour, if Labour bring forward a no-confidence motion, vote for it?

Baker: "At this point, I can foresee no circumstances while as a Conservative MP I voted against the government in a confidence motion.

"But we are apparoaching the point where the stakes are now so very high and so transcend party politics and what this country is about, and the fundamental British value that political power rests on consent, that I think these things are coming on to the table.

Coburn: "So it would be there?"

Baker: "It's on the table. There's no point denying things are running away."

It is possible that the Commons votes down May's government in a confidence motion, with the Tories then replacing her as leader in a bid to regain parliament's backing within the fortnight before an election is triggered.

MPs are set to take back control of the Brexit agenda today in a second round of "indicative" votes on a series of rival proposals tabled by backbenchers, to see if any can command a majority.

Tory MPs will have a free vote as they seek an alternative to May's deal, but Cabinet ministers will be told to abstain.

Alternatives on offer include a customs agreement with the EU, a second referendum on any deal and a power for MPs to vote to block a no-deal Brexit.

If a majority coalesces behind any plan, MPs are expected to seek to pass legislation on Wednesday to try to force the Government to act on it.

The move comes as May struggles to contain the rising tensions with her Cabinet as the clock counts down to the latest EU deadline on April 12.

Despite seeing her deal again defeated on Friday, the Prime Minister is determined to bring it back to the Commons for a fourth time in a final roll of the dice to get it over the line.

May spent the weekend trying to build support among MPs who could be won over, with aides saying she was "100% focused" on getting the result she needed.

Some in Parliament believe that if MPs begin to gather around a "softer" Brexit, it may finally convince Brexiteer hold-outs that the PM's deal now represents the "hardest" break with the EU available.

But Democratic Unionist Party Brexit spokesman Sammy Wilson insisted the party would continue to vote against May's EU withdrawal deal, which he said would "would take us away from the country that we fought to stay part of".

The pro-EU Justice Secretary David Gauke warned May not to ignore the will of Parliament if it does swing behind a "softer" deal such as the customs union plan proposed by Tory veteran Ken Clarke, which came closest to gaining a majority in the first round of indicative votes.

In an interview with the BBC, Tory chief whip Julian Smith said that the Parliamentary arithmetic means a "softer type of Brexit" is inevitable.

But the Prime Minister has set her face firmly against a customs union, warning it runs counter to the Conservatives' election manifesto and would inhibit Britain's ability to strike trade deals around the world.

If she were to give way, she would provoke a furious reaction from Brexiteers, with International Development Secretary Penny Mordaunt and Transport Secretary Chris Grayling among the ministers reportedly ready to resign.

Chief Secretary to the Treasury Liz Truss told BBC Radio 4's Today programme: "It's not clear to me that going softer is the way to command support."

She added: "If you look at the parliamentary arithmetic now, it's not clear that something like a customs union actually commands support."

Truss said: "I think that we are well prepared for no deal. I don't have any fear of no deal."

And prominent Brexiteer Jacob Rees-Mogg told LBC he was worried that May was "more concerned to avoid a no-deal Brexit than anything else" and might "decide to go for a customs union tacked onto her deal".

Rees-Mogg said May's Withdrawal Agreement might have won MPs' approval on Friday, when it was rejected by 58 votes, if the alternative had been a general election.

A letter to the Prime Minister signed by 170 Tory MPs demanded Britain leave by May 22 at the latest "without or without a deal".

In a sign of her waning authority, it was written by Brexit Minister Chris Heaton-Harris, according to The Times.