Liberal Democrat leader Sir Vince Cable has said his party will next week make a fresh drive to give MPs the chance to back a second Brexit referendum.

Sir Vince asked members of the new Independent Group for support as he sought backing for a motion aiming to lock a new public vote into law.

As it stands it is unclear whether any other group will try to bring forward or support a bid for a fresh referendum this Wednesday, when MPs will have another opportunity to table alternative proposals for the next steps in the Brexit process.

Some senior Labour figures have signalled their party might support a plan that would mean backing the prime minister’s Brexit deal in return for it being put to a referendum, but the idea may not be put to a vote in the Commons till further down the line.

Talking ahead of his speech to his party’s Scottish conference, the Lib Dem leader said: “For the good of our country, we will cooperate on areas of shared values, not least stopping Theresa May and Jeremy Corbyn’s chaotic and damaging Brexit.

“That is why I can announce Liberal Democrats will once again this week seek to secure cross-party support for an amendment in the House of Commons calling for a people’s vote, with the option to stay in the EU.

“We cannot let Theresa May or Jeremy Corbyn conspire to run down the clock. Liberal Democrats have led the campaign for a people’s vote. We have campaigned for it, we have marched for it and we will vote for it.”

With dissatisfaction over Brexit having sparked several Tory and Labour MPs to quit their party and form the Independent Group, Sir Vince said he has been speaking to “many of these now independent MPs” and that they have “much in common” with his party.

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The new group is set to meet on Monday to begin forming a policy platform, but despite many of its members having vocally backed a referendum, it is unclear whether they will back pushing for the Commons to vote in support of one at this point.

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 could 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.

The Independent has campaigned for a new public vote through its Final Say campaign, with its petition gaining more than 1.1 million signatures.