A Labour MP will launch a parliamentary bid for a public vote on the final Brexit deal, in a move that will add to growing pressure on the party’s front bench over its stance on leaving the EU.

Former trade minister Gareth Thomas is calling on the government to take back control from Brexit “ideologues” by letting the people determine the terms of Britain’s exit from the bloc through a fresh referendum in the autumn.

In a week set to be dominated by Brexit, Mr Thomas will use a 10-minute rule motion to test parliamentary support for a public vote, an idea he believes has cross-party backing.

It comes as Jeremy Corbyn faced calls to soften his stance and allow peers to back a crunch vote in the Lords on Tuesday, which would effectively keep the UK in the single market after Brexit.

Mr Thomas said he believed there was growing support in all parties for a vote on the final deal but acknowledged his bill was unlikely to become law.

He told The Independent: “Given that every analysis by the government shows Britain worse off under all possible variations of Brexit, and given claims of more funding for the NHS and other key services after we leave are now clearly false, the public should have the right to vote on whether to accept the final deal.

“As a former trade minister, I know that the trade deals ministers want to negotiate will involve significant immigration into the UK – a truth ministers have been reluctant to explain to those who voted Leave, for this issue.”

The Harrow West MP said he does not want to stop Brexit, adding: “A people’s vote would give the British people the chance to take back control over Brexit from a small cabal of Leave ideologues and instead to determine together our country’s economic, social and cultural futures.

“On an issue as significant as this for all our futures I believe the people of our country should have the final decision on whether the deal the government negotiates is good enough.”

Fellow Labour MP, Geraint Davies, has also brought forward a private member’s bill calling for a public vote, which will be heard in Parliament on Friday.

Both Labour and the Conservatives have ruled out allowing a further referendum but pro-EU MPs have been emboldened by recent defeats of the government in the Commons and the Lords, as well as a softening of Labour’s Brexit stance in favour of staying in a customs union with Europe.

Both Sir John Major and Tony Blair have backed another referendum but only the Liberal Democrats and the Greens are officially in favour.

It comes as pro-EU politicians accused the Labour leadership of ”cowardice” and adopting a “ridiculous” position by telling peers not to support a call for the government to negotiate a Norway-style Brexit within the European Economic Area (EEA).

Tory rebels told The Independent they have enough support to defeat the government if Labour joins them but party bosses have ordered peers to abstain – preventing it from being voted on in the Commons.

Brexit threatens life on the Irish border: in pictures Show all 15 1 /15 Brexit threatens life on the Irish border: in pictures Brexit threatens life on the Irish border: in pictures An abandoned shop is seen in Mullan, Co Monaghan. The building was home to four families who left during the Troubles. The town was largely abandoned after the hard border was put in place during the conflict. Mullan has seen some regeneration in recent years, but faces an uncertain future with Brexit on the horizon Reuters Brexit threatens life on the Irish border: in pictures A defaced ‘Welcome to Northern Ireland’ sign stands on the border in Middletown, Co Armagh Reuters Brexit threatens life on the Irish border: in pictures Mervyn Johnson owns a garage in the border town of Pettigo, which straddles the counties of Donegal and Fermanagh. ‘I’ve been here since 1956, it was a bit of a problem for a few years. My premises has been blown up about six or seven times, we just kept building and starting again,’ Johnson said laughing. ‘We just got used to it [the hard border] really but now that it’s gone, we wouldn't like it back again’ Reuters Brexit threatens life on the Irish border: in pictures Farmer Gordon Crockett’s Coshquin farm straddles both Derry/Londonderry in the North and Donegal in the Republic. ‘At the minute there is no real problem, you can cross the border as free as you want. We could cross it six or eight times a day,’ said Crockett. ‘If there was any sort of obstruction it would slow down our work every day’ Reuters Brexit threatens life on the Irish border: in pictures John Murphy flies the European flag outside his home near the border village of Forkhill, Co Armagh Reuters Brexit threatens life on the Irish border: in pictures Potter Brenda McGinn stands outside her Mullan, Co Monaghan, studio – the former Jas Boylan shoe factory which was the main employer in the area until it shut down due to the Troubles. ‘When I came back, this would have been somewhere you would have driven through and have been quite sad. It was a decrepit looking village,’ said McGinn, whose Busy Bee Ceramics is one of a handful of enterprises restoring life to the community. ‘Now this is a revitalised, old hidden village’ Reuters Brexit threatens life on the Irish border: in pictures Union Flag colours painted on kerbstones and bus-stops along the border village of Newbuildings, Co Derry/Londonderry Reuters Brexit threatens life on the Irish border: in pictures Grass reflected in Lattone Lough, which is split by the border between Cavan and Fermanagh, seen from near Ballinacor, Northern Ireland Reuters Brexit threatens life on the Irish border: in pictures Donegalman David McClintock sits in the Border Cafe in the village of Muff, which straddles Donegal and Derry/Londonderry Reuters Brexit threatens life on the Irish border: in pictures An old Irish phone box stands alongside a bus stop in the border town of Glaslough, Co Monaghan Reuters Brexit threatens life on the Irish border: in pictures Billboards are viewed from inside a disused customs hut in Carrickcarnon, Co Down, on the border with Co Louth in the Republic Reuters Brexit threatens life on the Irish border: in pictures Seamus McQuaid takes packages that locals on the Irish side of the border have delivered to his business, McQuaid Auto-Parts, to save money on postal fees, near the Co Fermanagh village of Newtownbutler. ‘I live in the south but the business is in the North,’ said McQaid. "I wholesale into the Republic of Ireland so if there’s duty, I’ll have to set up a company 200 yards up the road to sell to my customers. I’ll have to bring the same product in through Dublin instead of Belfast’ Reuters Brexit threatens life on the Irish border: in pictures A disused Great Northern Railway line and station that was for customs and excise on the border town of Glenfarne, Co Leitrim Reuters Brexit threatens life on the Irish border: in pictures Alice Mullen, from Monaghan in the Republic of Ireland, does her shopping at a former customs post on the border in Middletown, Co Armagh. ‘I’d be very worried if it was a hard border, I remember when people were divided. I would be very afraid of the threat to the peace process, it was a dreadful time to live through. Even to go to mass on a Sunday, you’d have to go through checkpoints. It is terribly stressful,’ said Mullen. ‘All those barricades and boundaries were pulled down. I see it as a huge big exercise of trust and I do believe everyone breathed a sigh of relief’ Reuters Brexit threatens life on the Irish border: in pictures A bus stop and red post box stand in the border town of Jonesborough, Co Armagh Reuters

Former shadow cabinet minister Chuka Umunna said it would “go against Labour’s progressive values” not to back the move in Parliament on Tuesday.

“Given the numbers of Conservative MPs now supporting the UK continuing to participate in the EEA, Labour is looking a gift horse in the mouth,” said Mr Umunna, a supporter of the pro-EU Open Britain campaign.

Labour’s Lord Alli, one of the signatories to the amendment, accused the party leadership of “complete cowardice” by ordering Labour peers to abstain.

But shadow international trade secretary Barry Gardiner told the BBC’s Sunday Politics: “The EEA option would actually have less control, we would be bound by the regulations but we would have no seat at the table in deciding what those regulations were.”