Zarah Sultana has said her new left-wing political party founded with Jeremy Corbyn is aiming at “running” the government despite high-profile splits emerging in the movement.

The Coventry South MP left the Labour Party in July to form a new group, operating under the temporary name Your Party, which she said was a “40-year project” and not a protest.

Her comments follow a difficult start for the party – which has attracted hundreds of thousands of sign-ups – but has been dominated by rows over leadership, finances and even its name.

Speaking to BBC’s Political Thinking with Nick Robinson, the MP said she wanted to “change people’s lives for the better”, which requires “winning state power”.

The new movement will be “socialist, democratic and member-led”, Sultana told the BBC.

And if elected, it would focus on “nationalising, building council homes, providing people with good secure jobs”.

She added: “I’m in politics because of a desire to change people’s lives for the better, and that means winning state power, that means actually running government.

“We’re building a party of the left that can win power and deliver justice.”

She added: “This is a 10, 20, 30-year project.”

In the four months since the fledgling party was announced it has been beset by disagreements and threats of legal challenges between the founding members.

Sultana’s interview came after three officials quit the board of MoU Operations Ltd (MoU) – set up to overseeing Your Party’s finances and membership – saying they were leaving her as the sole director.

The resignations follow reports the party is still trying to recover around £800,000 in donations and data held by MoU.

The problems stem from a schism in the party caused when Sultana launched a membership portal through its official email account, taking payment and data from an alleged 20,000 people.

Corbyn branded the emails “unauthorised” and urged supporters to cancel direct debits.

The membership portal was later replaced, but not before the dispute escalated into legal threats and accusations of a “sexist boys’ club”.

The pair have since reconciled.

Sultana has pushed for the party to be called The Left Party, while Corbyn hinted the name Your Party could stay.

Members will vote on the official name at a founding conference in Liverpool next month.

Sultana said she hopes to co-lead the new party with Corbyn, but will “throw her hat in the ring” if members opt for a single leader when the party constitution is agreed at conference.

During the interview, Sultana accused Reform UK leader Nigel Farage of having “all the features of a fascist politician”.

“I have legitimate concerns about what a Nigel Farage government would do to trade unionists, to working class communities, to minority communities, to LGBT people,” she said.

“When someone attacks trade union rights, when they are not supportive of minority communities, when they try to get us out of the European Convention on Human Rights so they can get away with anything, that is a descent into fascism,” she said.

A surge in support that has seen Reform UK opening up a 10-point lead in national polls reflects a wider crisis in politics, driven by voters left “angry” by years of austerity, she said.

Reform UK have been contacted for a response.

In order to “stop Reform,” Sultana said her new party will work with a resurgent Green Party.

Asked whether she would join the Greens, Sultana said she liked new leader Zack Polanski “but we are a different party”.

“There will be those alliances and those electoral pacts in the future,” she added.

Asked if her movement would split the left and take votes away form the traditional centre left voting base of Labour, Sultana said Labour “probably should have worried about that before it enabled genocide and passed through austerity”.

“The Labour party actually was quite content because it thought the left had nowhere else to go – and now the left has choices.”

You can listen to the interview with Zarah Sultana on the latest episode of Political Thinking with Nick Robinson on Saturday at 17:30 on BBC Radio 4 or on BBC Sounds.