Zarah Sultana and Jeremy Corbyn may be the figureheads of a new left-wing party, but already there is a battle over leadership.

The confusion behind the initial launch speaks to a wider debate happening behind closed doors as to who should steer the party – now and in the future.

Already, in the true spirit of Mr Corbyn’s politics, there is talk of an open leadership contest and grassroots participation.

Some supporters of the new party – which is being temporarily called “Your Party” while a formal name is decided by members – believe that allowing a leadership contest to take place honours Mr Corbyn’s commitment to open democracy.

They point out that under Mr Corbyn’s leadership of the Labour Party, members famously backed plans to make it easier for local constituency parties to deselect sitting MPs – a concept he strongly believed in.

His allies now say the former Labour leader, who is 76, is open to there being a leadership contest for the new party, possibly at its inaugural conference in the autumn, where names lesser known than himself can throw their hat into the ring.

“Jeremy would rather die than not have an open leadership contest,” one source familiar with the internal politics told Sky News.

However, there have been suggestions that Ms Sultana appears to be less keen on the idea of a leadership contest, and that she is more committed to the co-leadership model than her political partner.

Those who have been opposed to the co-leadership model believe it could give Ms Sultana an unfair advantage and exclude other potential candidates from standing in the future.

One source told Sky News they believed Mr Corbyn should lead the party for two years, to get it established, before others are allowed to stand as leader.

They said Ms Sultana, who became an independent MP after she was suspended from Labour for opposing the two-child benefit cap, was “highly ambitious but completely untested as leader” and “had a lot of growing into the role to do”.

“It’s not about her – it’s about taking a democratic approach, which is what we’re supposed to be doing,” they said.

“There are so many people who have done amazing things locally and they need to have a chance to emerge as leaders.

“We are not only fishing from a pool of two people.

“It needs to be an open contest. Nobody needs to be crowned.”

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While Mr Corbyn and Ms Sultana undoubtedly have the biggest profiles out of would-be leaders, advocates for a grassroots approach to the leadership point to the success some independent candidates have enjoyed at a local level – for example, 24-year-old British Palestinian Leah Mohammed, who came within 528 votes of unseating Health Secretary Wes Streeting in Ilford North.

Fiona Lali of the Revolutionary Communist Party, who stood in last year’s general election for the Stratford and Bow constituency, has also been mentioned in some circles as someone with potential leadership credentials.

However, sources close to Mr Corbyn and Ms Sultana downplayed suggestions of any divide over the leadership model, pointing out that their joint statement acknowledged that members would “decide the party’s direction” at the inaugural conference in the autumn, including the model of leadership and the policies that are needed to transform society.

A spokesperson for Mr Corbyn told Sky News: “Jeremy will be working with Zarah, his independent colleagues, and people from trade unions and social movements up and down the country to make an autumn conference a reality.

“This will be the moment where people come together to launch a new democratic party that belongs to the members.”

Sky News has approached Ms Sultana for comment.