The shadow chancellor, John McDonnell, has rejected claims that he has been urging Jeremy Corbyn to sack his two most senior aides because they are opposed to Labour committing to backing remain in a second referendum.

Insisting that he had not called for anyone to sacked, McDonnell claimed stories about a split between him and Corbyn were a “myth” promoted by journalists prone to exaggeration.

But he also accepted that he and Corbyn did “disagree on things” and that Corbyn was in a different position because as party leader he had a duty to “build consensus”.

Earlier this year, in response to fears it was losing support to pro-remain parties such as the Liberal Democrats, Labour shifted its Brexit stance and agreed that any Brexit deal passed by parliament should be put to the people in a second referendum. But the party has not committed to backing remain if such a referendum were to take place. McDonnell said last month he was arguing the case for Labour to explicitly back remain.

Diane Abbott, the shadow home secretary, has previously said publicly that she is “beginning to worry” about party policy not being sufficiently remain, and on Sunday the Sunday Times claimed she and McDonnell had both urged Corbyn to sack his two advisers seen as being most resistant to a policy shift: Karie Murphy, his chief of staff, and Seumas Milne, his head of strategy and communications.

Asked about the story, McDonnell told the BBC’s Andrew Marr Show: “I’ve not said to sack anybody. Look, it’s July. What happens in July in parliament? Journalists, the lobby, stagger from reception to reception drinking some of the most nauseating wine that’s ever been produced from a grape. What then happens, they exaggerate and invent stories and that’s what’s happened here.”

McDonnell went on: “Jeremy and I talk about policies on a daily basis. Yes, we’ll disagree on things, but we’ll then come to an agreement. He’ll build consensus, just as he always does, and then we back each other up.”

Abbott told the Sunday Times in a statement that she did not believe sacking any member of Corbyn’s staff would help the Labour cause.

In a separate interview on Sky, Barry Gardiner, the shadow international trade secretary, appeared to refine his position on whether Labour was a remain party. In March he said Labour was “not a remain party now”, but on Sky he said: “We have always been a remain and reform party.”

Gardiner played down the prospect of Labour calling a no-confidence vote in the government before the summer recess, saying the party would call the vote when Tory MPs were likely to support it.