Zarah Sultana has said she and Jeremy Corbyn have patched up their combustible co-leadership of a new leftwing party, with the MP comparing the duo to Liam and Noel Gallagher.

Speaking alongside Corbyn at The World Transformed political festival in Manchester, the Gallaghers’ home city, Sultana insisted they could cooperate over the organisation still only known, unofficially, as Your Party.

“Obviously you’ve all seen what’s happened over the past few weeks but I’m here to tell you the show is back on the road,” said Sultana, the Coventry South MP who was elected on a Labour ticket but now sits as an independent.

“I know that I’m in Manchester, so I have to reference Liam and Noel Gallagher. If they can do it, of course me and Jeremy can.

“The only difference between us is that Jeremy still thinks Arsenal are still going to win the Premier League, and we know that they will always come second place with a second-place trophy.”

The status of the new party, also billed as a grassroots membership organisation, has been in doubt for weeks after Sultana and Corbyn, the former Labour leader who was re-elected last year as an independent MP, fell out bitterly over its organisation.

This reached its lowest point last month when Sultana said she had consulted defamation lawyers after a very public spat with Corbyn about her decision to set up a paid membership system for the party.

Corbyn said the payment site had been set up without approval, describing it as a “false membership system” that collected money and data without authorisation. He said he had referred the matter to the Information Commissioner’s Office.

In response, Sultana said she had been frozen out of the new party by a “sexist boys’ club” consisting of Corbyn and four pro-Gaza independent MPs.

Sultana swiftly rescinded the threat of legal action, saying she was in talks with Corbyn and wanted to reconcile.

A subsequent video message by Corbyn to the mailing list of 750,000 people who had expressed interest in the party apologised for events but made no mention of Sultana, while the video showed her only fleetingly.

The leftwing World Transformed event used to run in parallel with the Labour conference, but is taking place this year after Labour’s event ended in Liverpool.

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Also appearing was Zack Polanski, the new leader of the Greens, a party with whom Sultana has been linked as a possible recruit. Polanski recently told his party conference that the Greens were going to challenge Labour because Keir Starmer would “hand this country on a plate” to Nigel Farage.

Speaking at the event on Friday, Sultana accused Farage of “peddling racism” to distract people from other events.

“The truth is, Reform is just another wing of the political establishment,” she said. “Funded by billionaires and aristocrats, fronted by a millionaire stockbroker, an ex-public schoolboy, Nigel Farage. He is peddling racism to distract us from the real agenda: more privatisation, more deregulation, more handouts for the rich, more cuts for everyone else.”

Corbyn said his new party would need to work with the Greens and local independent parties.

He said: “There are going to be opportunities and points where we need to work with the Greens. There may be points where sometimes we don’t agree with the Greens. So we have our identity, we have our principles, and we have our position, but we’re anxious to make progress in our society, and that will mean working with a lot of different people – nothing wrong in that.”