A tense meeting of Labour’s shadow cabinet failed to agree any advance on the party’s position on a second Brexit referendum, despite several senior figures saying they had been led to believe Jeremy Corbyn would soon give full-throated backing for remain.

Corbyn is understood to have told shadow cabinet ministers there would be further consultation with the unions and a decision on the next step taken in the coming weeks, to the frustration of several present including the shadow chancellor, John McDonnell.

Sources in the room said McDonnell had said he was “under the impression we were making the decision today” on how to advance Labour’s position. The shadow foreign secretary, Emily Thornberry, also questioned why a decision was not being taken and said it was “about showing leadership”.

Several shadow cabinet members emerged from last week’s meeting believing the party would agree a new strategy on Tuesday, after Corbyn had consulted trade union leaders.

“Basically Unite stepped in yesterday and put the brakes on,” one shadow cabinet source said. McDonnell “is obviously trying to push us forward but LOTO [the leader’s team] are pushing back”.

Speaking at a car industry conference on Tuesday, McDonnell was asked directly if the Labour party was campaigning for a second referendum, replying: “Well, I’m arguing the case … The discussion we are having in the Labour party now, and it is no secret, is what would our attitude be if there is a referendum?”

“I’ve said personally, I’d vote for remain. I campaigned for remain because I can’t see anything better than what we have got at the moment. I can see the consequences in terms of jobs and living standards.”

McDonnell said the party’s policy would “evolve over the next week or so because there are more party consultations”.

Phil Wilson, a backer of the People’s Vote campaign who has co-led attempts in parliament to put any Brexit deal to a referendum, said the delay was damaging the party.

“Labour members and Labour MPs expect our party to have a clear policy that reflects our values,” he said. “Instead, we have to listen to muddle, confusion and the sound of the can being kicked listlessly down a never-ending road. The longer this dithering goes on, the more damage will be done to our party.”

The shadow cabinet rift comes amid concerns about a summer of potential selection battles after MPs were given a fortnight to decide whether they wished to stand again for parliament – a sign that the party is preparing for a snap election.

MPs suggested it could make the party impossible to manage, with frontbenchers among those expressing concern they could be deselected.

“We could end up in a situation where frontbench Labour MPs are deselected and have to serve for another three years knowing they will have to go at the next election,” one MP said. “How does that serve the party or help departmental teams develop a manifesto? How can whips manage a party where 20 MPs may have been deselected? Either senior Labour people know this and don’t care or they don’t realise. That is very worrying.”

MPs expressed anger at the timetable at a private meeting of Labour MPs on Monday night. The chair of the parliamentary Labour party, Jon Cryer, told the meeting it was a “rushed job” to give MPs only two weeks to decide whether to stand again when they would normally be notified well in advance.

Many MPs have also questioned the need for such a short timeframe, with several contrasting it with the leadership’s apparent unwillingness to ballot members on a change of Brexit policy, as proposed by the deputy leader, Tom Watson.

“It’s striking that, in this time of political chaos, our leadership can’t agree to give members a ballot on Brexit and what our policy should be, but can make time to push for them to happen on deselections of MPs – I know which I would rather be fighting,” one MP said.

Party rules were changed in September to make it easier for a local party to “trigger” a selection contest, rather than automatically re-adopting the sitting MP.

Several MPs said they had already begun the groundwork preparing for trigger ballots, but warned that reselection battles would take huge amounts of time and energy. “This is money and time that could go into holding my marginal seat at snap election,” one MP said.

Another called the new procedure “a massive distraction”.

The flashpoints where party sources said MPs are most at risk of selection battles include Thangam Debbonaire’s seat in Bristol West and a number of seats around Merseyside and the north-west, including the seats of Maria and Angela Eagle and Louise Ellman.

Roger Godsiff, the MP who has defended parents’ rights to take their children out of LGBT-inclusive lessons, and Kate Hoey, who has voted consistently with hard Brexiters in parliament, could also face local difficulty if they decide to stand again.

It is unclear what would be the fate of two Labour MPs who are suspended from the party and are under investigation – Chris Williamson and Kelvin Hopkins. When the snap election was called in 2017, the suspended Labour MP Simon Danczuk was deselected.

At least two Labour MPs who have previously rebelled to back efforts to deliver Brexit, Jim Fitzpatrick and Ronnie Campbell, have already announced they will not seek re-election.