Jeremy Corbyn has faced down a challenge spearheaded by his deputy, Tom Watson, for Labour to signal its unequivocal backing for a second Brexit referendum in the forthcoming European election campaign.

In a move that sparked an immediate backlash among remain-supporters, Labour’s ruling national executive committee (NEC), announced that its manifesto for the election would be “fully in line” with its longstanding policy.

That means continuing to support “Labour’s alternative plan” for Brexit – “and if we can’t get the necessary changes to the government’s deal, or a general election, to back the option of a public vote”, a Labour source said.

The wording falls well short of the position set out recently by Watson, and by the shadow Brexit secretary, Keir Starmer, who told the House of Commons in April: “At this late stage it is clear that any Brexit deal agreed in this parliament will need further democratic approval.”

Some Labour MPs reacted with fury to the NEC’s decision. Bridget Phillipson, who represents Houghton & Sunderland South, speaking for the People’s Vote campaign, said: “The manifesto’s mealy-mouthed wording still maintains the fiction that there is a deal out there that can satisfy all the promises made three years ago, avoid real costs to jobs and living standards, or end the endless crisis around Brexit.

“This means Labour risks demoralising activists, depressing turnout among supporters and decreasing the share of the vote for candidates who – like the overwhelming majority of our party – are fighting for a people’s vote on any Brexit deal.”

The cautious restating of Labour’s stance comes as cross-party Brexit talks with the government enter a critical phase, with both sides insisting there is fresh impetus behind the attempt to find a consensus.

Negotiations are expected to resume on Wednesday, with Downing Street setting an informal deadline of the middle of next week for significant progress to be made.

The Tories have been stung by a string of recent polls suggesting public support has collapsed since the decision to delay Brexit for a second time. An Opinium poll for the Observer this week had Labour level-pegging with Nigel Farage’s Brexit party on 28% of the vote, with the Conservatives on just half that level.

Labour’s divisions on Brexit have been exposed afresh by the row over the party’s European manifesto, which earlier involved Watson staging what he insisted was a “polite” walkout of a meeting of the shadow cabinet, after members were told they would not be handed a draft.

Corbyn is keen to avoid Labour being pigeon-holed as a remain party, not least because he hopes to make significant gains at Thursday’s local elections, including in Brexit-supporting areas.

But he is under intense pressure, not just from Watson, Starmer and the shadow foreign secretary, Emily Thornberry, who has also made clear she would like a referendum on any Brexit deal, but from an increasingly vocal group of leftwing MPs, including Clive Lewis and Rachael Maskell.

MPs from both sides of Labour’s Brexit divide claimed victory after the meeting. Referendum-supporters seized on the fact that the statement said Labour would “back the option” of a public vote, rather than keep it “on the table”.

Wes Streeting, the MP for Ilford North, tweeted: “Glad the NEC made the right call and confirmed that a public vote will be in our manifesto.”

But MPs in leave-supporting seats, including Gloria De Piero, who represents Ashfield in Nottinghamshire, cheered the fact that a referendum would be merely “an option” for Labour, if talks with the government break down.

A Labour spokesperson said: “Labour is the only party which represents both people who supported leave and remain. We are working to bring the country together after the chaos and crisis created by the Tories.”

The meeting followed a public spat last week when some Labour MPs reacted angrily to a draft leaflet for the European elections that failed to mention a referendum.

Corbyn was supported at the lengthy meeting inside the party’s Southside headquarters in Victoria, London, by a clear majority of NEC members, including all of those backed by Momentum, the grassroots pro-Corbyn campaign group.

Just one vote was held, on an amendment proposed by the TSSA union, that would have committed Labour to a “confirmatory” referendum on any Brexit deal – even if the government caves in to all Labour’s demands. It was rejected by a “clear” margin, NEC sources said.

Manuel Cortes, the TSSA’s general secretary, described the outcome of the meeting as, “Labour’s latest Brexit fudge”, adding that the party’s “unicorn demands” for a Brexit deal, would “in effect make us a rule-taker colony of Brussels”.

“That’s the naked truth and we have missed an opportunity to tell it to voters like it is. We face a stark choice – a no-deal economic crash, vassalage or the best option, no Brexit at all,” he said.

However, some senior party figures drew comfort from the fact that the NEC is not meant to be a policymaking body; and the process for agreeing a general election manifesto would be different, involving shadow ministers in setting policy for their respective brief.

One NEC member said: “Politically, it was necessary for some people to turn this into a fight about a second referendum but in reality this meeting was not going to change party policy.

“If we have a general election manifesto meeting when we need to decide a policy on a second referendum, it will be very different, but most people are happy to have this compromise right now.”

The breakaway Change UK group seized on the outcome of the NEC meeting. Mike Gapes MP, the former Labour MP who is the party’s foreign affairs spokesman, said: “If you’re a Labour supporter and dismayed by Labour’s latest fudge on Brexit, send Corbyn a message by lending Change UK your vote.”