A senior Tory has demanded a free vote on a second Brexit referendum so the “very, very many” ministers who back it can express their support in the Commons.

Sarah Wollaston urged Theresa May to give frontbenchers free rein when MPs vote on alternatives to her own Brexit ‘plan B’ on January 29, claiming many in the party are “absolutely determined” to stop a no-deal.

Appearing on HuffPost’s Commons People podcast, the Commons health committee chair said she wanted Tories to be free to back an amendment she is tabling to test support for a so-called ‘people’s vote’.

It comes after reports that cabinet ministers have been pushing for a free vote on a fresh referendum.

Ministers such as work and pensions secretary Amber Rudd have already said all ‘plan B’ options should be on the table after May’s deal was rejected by a record 230 votes on Tuesday.

Wollaston’s amendment could mean the first Commons vote on a second referendum since the idea starting gaining real momentum as the huge scale of opposition to May’s deal became clear before Christmas.

She told Commons People: “I really hope what the prime minister will do is to make it a free vote on the Conservative side.

“Because there are very, very many colleagues I speak to who would like to back this.

“There are some colleagues who in their hearts want to back it now but feel like they have to justify to their associations and their constituents more widely that every other avenue has been exhausted.

“They are firmly of the view that’s where we’ll end up in the end.

“They are absolutely determined they will not be supporting or be part of something that delivers no deal.

“We could get there, I think, with a free vote on the Conservative side but it might just take another step in the process to make it absolutely clear that all the other options are out of the way.”

Wollaston acknowledged there are currently not enough MPs to form a majority for a ‘people’s vote’, but stressed her amendment would force Jeremy Corbyn into a decision on the issue.

She accused Corbyn of trying to row back on party policy which states that if he fails to force a general election, Labour must then “support all options remaining on the table, including campaigning for a public vote”.

The Labour leader has made clear he is ready to table repeated no-confidence motions in the government despite losing in his first attempt to force an election on Wednesday.

He will also table his own amendments to May’s plan B, putting forward his preferred solution of a customs union.

But Wollaston told Commons People: “(My amendment) will give the Labour leadership a week at which to decide what are they going to do? Are they going to get behind this or not?

“If they do not get behind it at that point I think there will be huge irritation because although it might not work at the first attempt, it cannot work until it has official Labour Party backing.”

She added: “Jeremy Corbyn has got to stop saying different things to his different voter bases and carry out the wishes clearly expressed and clearly promised that after the no confidence vote they would move to supporting a ‘people’s vote’ or a public vote as they refer to it.”