Labour has admitted it will not support a new referendum on Brexit in all circumstances, in a major blow to those in the party campaigning for one.

Sources close to the Labour leadership confirmed that the party is not advocating a referendum on anything other than a “damaging Tory Brexit” and will not support one if Britain leaves the EU on terms that Labour backs.

The Independent has learnt that the issue was the subject of a row between Mr Corbyn’s shadow ministers that pitted Keir Starmer and Emily Thornberry against Brexit-backing frontbenchers led by Jon Trickett.

As it dawned on Labour Remainers today, a prominent MP who backs the People’s Vote campaign warned that a failure of the party to follow through on the pledge to back a new referendum would be seen as a “betrayal”.

It comes as deputy leader Tom Watson is in the process of forming a new “social democrat” group within the party, while eight MPs have quit the party, in large part over Brexit policy, to form the new Independent Group.

Labour said last week that it would support a vote on any “credible” exit plan passed by parliament, and shadow ministers took to the airwaves to promise to demand a “confirmatory referendum” on “whatever deal may or may not pass through parliament”.

However, sources have now told The Independent that the party will only support a referendum on a “damaging Tory Brexit” deal. Crucially, it is understood that Labour does not consider this to include the type of arrangement being proposed by former Conservative ministers Sir Oliver Letwin and Nick Boles, who Mr Corbyn held talks with yesterday. Their plan would keep the UK in the single market and a customs union with the EU.

The revelation will prompt speculation that Mr Corbyn’s priority remains building Commons support for a softer Brexit deal that and refusing to allow the public a Final Say vote.

The confirmation that the party will only support a public vote on Theresa May’s deal and not on other forms of Brexit is likely to infuriate the party’s pro-EU MPs, who believed they had secured backing for a vote on any deal.

Responding to the news, Cardiff South and Penarth MP Stephen Doughty warned Mr Corbyn that Labour voters would feel “completely betrayed” if Labour did not agree to put any Brexit deal to a public vote.

He said: “The overwhelming majority of Labour voters and members support a public vote on any deal – the unanimously agreed policy of party conference – and warmly welcomed Keir and Jeremy’s commitment on this just days ago.

“Now that we know just how badly any sort of Brexit will hit jobs and public services, and we see billions being wasted, instead of being spent on our NHS and more police, Labour voters and members would feel completely betrayed if the party in any way were seen to be working with the Tories to enable Brexit, whether by voting for the PM’s disastrous deal, or by helping to stitch up another deal behind closed doors without putting that back to the people for their final say.”

The Independent understands that the party’s policy on another referendum was the subject of a fierce debate between senior shadow ministers at a Labour Brexit sub-committee meeting last week.

Sources said Sir Keir Starmer, the shadow Brexit secretary, and Emily Thornberry, the shadow foreign secretary, had pushed for a referendum on any deal agreed by parliament but that others, led by shadow Cabinet Office minister Jon Trickett, insisted it should only support a public vote only on Ms May’s deal.

Shortly afterwards, Ms Thornberry told Channel 4 that Labour would demand a referendum on any Brexit deal, saying: “We would have a referendum on whatever deal may or may not pass through parliament, and we would be saying to people, ‘Do you want this? Or do you want to Remain?’ “It would be a confirmation referendum, a bit like what happened with the Good Friday Agreement.”

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But the Labour leadership has rowed in behind Mr Trickett after a strong backlash from dozens of Labour MPs in Leave-voting areas, who have vowed to oppose any fresh referendum.

One MP said: “There are a lot of people who are really angry. At this point we should be pushing for a deal.

“Some have already said they won’t support another referendum but there is a larger group that might go with the whip but are just really worried about the direction we’ve taken.”

Ian Lavery, the party chairman, has also raised strong concerns about the party’s position, warning the shadow cabinet this week that Mr Corbyn would not become prime minister if the party backed a fresh referendum.

Mr Corbyn said yesterday that his meeting with Sir Oliver and Mr Boles, together with Labour’s Lucy Powell and Stephen Kinnock, had left him ”more certain than ever” that a Brexit deal could be agreed.

Writing for the Daily Mirror, he said: “Yesterday, I saw senior Labour and Conservative MPs to discuss a close economic relationship with the EU, which would help protect jobs like those of the Honda workers in Swindon, some of whom I also met.

“I left both meetings more certain than ever that we can find a way to work across parliament to force the government to back a sensible Brexit plan that protects jobs and more determined to achieve it.

“I will continue to reach out to get a decent Brexit deal so our country can spend more time talking about our children’s future than a customs union.”

Appearing to shift away from backing a fresh referendum, the Labour leader said a soft Brexit deal was “the best Brexit compromise for for both 17 million Leave voters and 16 million Remain voters”, adding: ”But we can’t accept a damaging Tory Brexit or a no deal outcome, so we also support preparing for a public vote in case parliament is not able to achieve a sensible Brexit.”

Labour will table its own bid for second Brexit referendum within a fortnight says McDonnell

Mr Corbyn’s latest attempts to help pave the way for a Brexit deal are likely to anger party members and many MPs, who insist it should be focusing its attention on a fresh referendum that could stop Britain leaving the EU.

While the “Common Market 2.0” proposal being pushed by Sir Oliver and Mr Boles is not identical to Labour’s own preferred plan, there is a significant degree of overlap, raising the prospect of a cross-party consensus for a soft Brexit.

MPs will vote on Ms May’s proposed deal next week. If it is rejected a second time, the government has promised to let the Commons vote on whether to pursue a no-deal outcome or seek to extend the Article 50 process.

A Labour spokesperson said: “The best outcome for the country is an immediate general election that can sweep the Tories from power.