Jeremy Corbyn’s spokesman has insisted the Labour leader makes his own decisions, as he hit back against claims by Margaret Beckett that some of Corbyn’s close aides wanted Britain to leave the EU, “no matter what”.

Beckett, a former foreign secretary who is campaigning for a second referendum, said she thought the Labour leader was open to the idea but some of his closest advisers were preventing him from budging and would be prepared to allow a no-deal Brexit.

“I don’t get the impression that Jeremy himself is the stumbling block,” she told BBC Radio 4’s Today programme. “There are people very close with great influence on him who are passionately opposed to it … and he wants to keep the party together as much as possible.

“Unfortunately, it’s looking more and more that some of the people who he wants to accept the majority view are not just expressing reservations but completely oppose, and I’m beginning to think some of them do actually want Britain to leave no matter what and they don’t give a toss.”

Corbyn’s spokesman rejected that idea. “Reaching back into political history, I think we’re all familiar with the trope about good kings and their bad advisers”, he said. But he added: “The idea that Jeremy doesn’t make his own decisions is laughable.”

The spokesman said Corbyn was continuing to consult with trade unions and members of Labour’s national executive committee about the party’s Brexit policy.

“Jeremy is trying to make sure that there is wide consultation in the Labour movement. That includes the affiliated trades unions who have 49% of the vote at Labour party conference, and they are a vital part of our party.

“It’s a consultation to try and find a position that the party can unite around.” He said that process would be completed “in the next few weeks”.

He said there was already a consensus over avoiding a no-deal Brexit and over the shift towards advocating a public vote on any deal, as announced by Corbyn after last month’s European elections.

But he added that there was still no agreement about what could be on the ballot paper in any referendum Labour might support, and whether the party would now commit to campaign for remain.

He added that a referendum was “not the only part of our policy on Brexit. We want to see a general election. We want to see a public vote on any deal. Our alternative compromise plan is still on the table.”

Beckett declined to say which advisers and Labour figures she was talking about.

Shadow cabinet ministers had been expecting Labour’s position to move to full backing for a remain position in a second referendum at a meeting on Tuesday.

But Corbyn is understood to have told shadow cabinet ministers there would be further consultation with unions and a decision on the next step 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”.

“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 whether the Labour party was campaigning for a second referendum. “Well, I’m arguing the case,” he replied. “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.”