A crucial chance for MPs to back giving the British public a Final Say referendum on Brexit next week could be missed with no one yet committed to tabling a motion calling for one.

Backers of the People’s Vote campaign are leaning towards a plan which would not see MPs asked to support one until the very last minute, probably in a couple of weeks’ time as Ms May puts her finalised deal before the commons.

Meanwhile, the new Independent Group of MPs are set to meet on Monday to decide whether to support that idea or to table their own amendment now calling for a new referendum.

Either way pressure is building on Labour leader Jeremy Corbyn to give more than lukewarm support to a new public vote to stop any more MPs quitting his party over its Brexit strategy.

Under the process already approved by parliament, unless Theresa secures a new deal in the coming days – which currently seems unlikely – she must on Wednesday allow other MPs to put their own plans to commons votes for the next steps in the Brexit process.

As well as a likely amendment on delaying Brexit backed by Labour’s Yvette Cooper and ex-Tory minister Oliver Letwin, there has been speculation over whether MPs might finally have a chance to back a new public vote – after missing out on two previous opportunities.

But some Labour MPs who had previously given support to the People’s Vote campaign are now filing in behind a proposal put forward by Labour MPs Peter Kyle and Phil Wilson – which would see them again pass on the opportunity to force a new referendum next week, and instead vote for Ms May’s withdrawal agreement later down the line as long as she agrees to put it to a public vote.

One source close to the plan said: “A lot of people are talking about Wednesday as high noon, but it’s not high noon. People who want a referendum have always been clear that it would be best if it is the last option standing, so waiting before voting on it makes sense.”

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Both shadow Brexit secretary Keir Starmer and shadow chancellor John McDonnell have met with the plan’s advocates, who are arguing that unless Mr Corbyn also backs it he will face further resignations form his benchers.

But another MP who has spoken out in favour of a new referendum is frustrated at the approach, arguing that it creates further delay and also that it is politically unrealistic to think Mr Corbyn would support any plan involving him backing Ms May’s deal.

The MP said: “If the goal is to force Jeremy to put his cards on the table over another referendum then let’s put down an amendment now. If he refuses, more people will resign and then you can still back the Kyle/Wilson plan later on.

“Putting it off until the meaningful vote on May’s deal, whenever that comes, just gives him more time to procrastinate.”

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The other group who might move quicker and push MPs to vote to back a referendum on Wednesday is the Independent Group, made up of eight ex-Labour and three ex-Tory MPs, the majority of whom have been vocal supporters of a new public vote.

But with fledgling grouping still without a leader or a formed policy prospectus it is unclear whether they will move a motion this week.

One of their number told The Independent: “We are having a meeting on Monday and we need to see what comes out of that. There are a lot of people there who want a second referendum, but we need to decide what the best approach is.”