The Labour MP Chuka Umunna has sought to scotch rumours that he hopes to use the People’s Vote second referendum campaign as a platform for launching a new political party.

After days of speculation about his future within Labour, Umunna said his priority was to stop Brexit as talks with the European Union reach their decisive stage over the autumn.

“The idea that the People’s Vote campaign is a precursor to a new party is complete and utter bollocks,” Umunna told the Guardian. “Frankly people need to stop spreading false news about this.”

Umunna has been frequently touted as the leader of a group of MPs who are unhappy with Jeremy Corbyn’s leadership and have contemplated breaking away from Labour since 2015. Other former frontbenchers in the group, including Chris Leslie, have shared their views and feelings on a WhatsApp group known as the Birthday Club.

Umunna’s remarks reflect the fact there is insufficient consensus among disaffected MPs about quitting Labour. He is also under pressure to ensure the anti-Brexit campaign is not weakened by speculation that it represents a Trojan horse for other political ambitions.

“The People’s Vote campaign contains people from all parties and people of no affiliation at all – that’s the reason it has been successful,” Umunna said. “People need to stop speculation that aids and abets Jacob Rees-Mogg, Nigel Farage and others.”

To have maximum impact, a breakaway party would need to become the third largest party in Westminster, exceeding the Scottish National party’s 35 MPs. This would give it access to public money to spend on researchers and enhanced privileges in the Commons, for example, the right for its leader to put two questions to the prime minister every week.

Few in Westminster believe there are more than a handful of Labour MPs who are prepared to walk – although the party’s turmoil over antisemitism has unsettled a wider group of MPs to the point where some have considered their long-term future in the party. Some of those MPs believe it would be strategically wiser to make their move at the conclusion of the Brexit process.

One name mooted by several sources for a centre party is Back Together, although this was dismissed by some of those close to the conversations.

To outnumber the SNP, any new grouping would also require the participation of the Liberal Democrats, who hold 13 seats in parliament. But allies of Vince Cable say that while the party leader has been keen to meet disaffected Labour MPs and see what opportunities there are for his party, he is not willing to propose an alliance or merger.

Andrew Adonis, one of those involved in the breakaway Social Democratic party before he later joined Labour, said he believed the mooted centre party would have no chance under Britain’s first-past-the-post political system because a split in Labour would not amount to a sufficient base of support among the electorate.

Writing for the Guardian, the peer said a centre party would also require support from Conservatives. “Unless the Tory party splits – and I see no sign of it – a new party will almost certainly fail to break through,” the peer wrote, adding he had no intention of leaving Labour.

The Conservative MP most frequently touted as a potential defector is Anna Soubry, an anti-Brexit campaigner who is close to Umunna and worked with him in the People’s Vote group. But she has repeatedly denied she would leave the Tories despite her unhappiness with Brexit. “It is my intention to stand again in Broxtowe as a Conservative candidate,” she told the Guardian last month. “I just want my party back, please.”

A change of Tory leader may prompt a change of thinking among some wet Conservatives. The former attorney general Dominic Grieve said earlier this month he would quit the party if Theresa May was ousted and Boris Johnson became leader, but for the moment that remains only a theoretical possibility.

Some Corbyn allies have also raised the idea more than once that a breakaway party is under active consideration. A week ago, the Unite general secretary, Len McCluskey, accused Umunna of exploiting the antisemitism row within the party “to justify his moves to break away from Labour, the plotting for which has been widely reported elsewhere”.

Meanwhile, in an apparent reference to Umunna, the shadow chancellor, John McDonnell, tweeted that “for anybody to use the issue of antisemitism as a cover for launching a new political party they had been planning for nearly two years would rightly be seen as an act of appalling cynicism”.

For anybody to use the issue of antisemitism as a cover for launching a new political party they had been planning for nearly two years would rightly be seen as an act of appalling cynicism, basely exploiting a genuine concern that people of goodwill are working hard to address. — John McDonnell MP (@johnmcdonnellMP) August 16, 2018

At the end of last week, Umunna responded by saying he “won’t be bullied” and followed up by making a speech on Tuesday on teenage stabbings in which he said the “populism of the left and right” cannot solve the problem of serious youth violence and that “a paradigm shift” in thinking was required.