Plans to hand parliament control of Brexit received a boost after senior Labour figures indicated the party could swing in behind them.

A shadow cabinet member told The Independent it was “possible” that Jeremy Corbyn’s party could back the move, while a string of Labour MPs also said they were more inclined to back it as it evolved.

One of the authors of the plan claimed on Friday that it is also backed by cabinet ministers, and that up to 20 more junior front benchers had said they would quit if Ms May whipped them to vote against it.

The proposal headed by Nick Boles would see Article 50 extended possibly to the end of the year to prevent a no-deal Brexit in March if no agreement has been approved by parliament by then.

It would need significant Labour backing to pass through the commons when it is likely put to a vote on 29 January, but it has been unclear if that would be forthcoming

However, one shadow cabinet member said: “Theresa May may be the prime minister but she does not command a majority in this house.

“We will try with others to see where a majority might be, so this is possible.”

Shadow chancellor John McDonnell also said earlier this week that the party would need to consider extending Article 50.

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The Independent understands that Labour will also table its own plan on 29 January for what should happen next, though this would be unlikely to attract Conservative support.

The Boles plan had also included measures to hand power for directing Brexit to a cross-party parliamentary committee headed by a senior Conservative MP.

But this was stripped out on Wednesday night leaving it more focussed on facilitating a mechanism for delaying Brexit if no deal is looming.

Other Labour MPs also signalled that they could fall in behind the plan, with one saying: “It’s not my first choice, but it’s an option. I’d like to see if a People’s Vote amendment goes down.

“However, obviously everyone wants to stop no deal, and if this helps then ok.”

Jeremy Corbyn says Labour is not ruling out a 'public vote' on the future of Brexit

But some in the People’s Vote movement still see the longer extension proposed by the Boles plan as a threat to gaining a second referendum.

One backer said: “A short extension for a People’s Vote is our goal, not a long extension to facilitate a softer Brexit further down the line – it feels like it’s about facilitating Brexit in a different way.

“But it is a way that will undermine a Peoples Vote and the momentum that has built up behind it.”

Ms May will make a statement on her plans on Monday, as expected, but voting on her motion will not be allowed for another eight days.

Mr Boles told The Standard earlier in the day: “A large single-digit-number of cabinet ministers have told me they will not vote against the amendment.