Ed Miliband is facing a renewed civil war between the Blairite wing of his party and its union backers after an attempt by the unions to ban Progress, the pressure group most closely associated with Tony Blair.

The attack on Progress appears to involve many unions, and is being described by the union Unite in internal documents as part of a "struggle for Labour's soul".

Progress is funded by Lord Sainsbury, one of Blair's biggest champions. Its president is the shadow education secretary, Stephen Twigg, but it is denounced by some on the left as neo-liberal.

A Unite strategy document dated December 2011 identifies Progress as a force opposed to its plan to transform Labour. It states: "Labour party policies are often determined by a small group of advisers – far too often dominated by old thinking, neo-liberalism and the organisation Progress."

It adds: "The battle for Labour's future direction is therefore undecided, and it is right that Unite, as the party's largest affiliate, should play the fullest possible part in the struggle for Labour's soul."

The row is deeply worrying for party officials because Blair is due to make a speech soon that is being described as his re-entry into British politics. Miliband is also due to speak at a Unite conference in a fortnight's time.

Labour's national policy forum meets . Ed Miliband will tell it that "the old orthodoxies about our economy, our society and our politics are crumbling before our eyes". He will argue that the Leveson inquiry into media standards has become a "symbol of what is wrong with politics. Not just a media scandal, but a scandal about the way Britain is run, in which unaccountable power was exercised by some newspapers". He will describe David Cameron as the "tainted prime minister" because of his relationship with News International executives.

He will also suggest that the appointment of Jon Cruddas as Labour's policy review chief will mean a reordering of the review into three core headings: economy, society and politics. The reorganisation appears to be an implicit acknowledgment that the previous structure was too disparate and unwieldy.

The row over Progress comes in the week that Paul Kenny, the GMB general secretary, said that a motion was being drawn up for this autumn's party conference designed to ban Progress from the party. A lengthy 16-page leaflet attacking Progress has also been sent anonymously to the home addresses of Labour councillors and constituency secretaries.

An offer by the Unison union's south-east region to let its headquarters be used for a Progress meeting next weekend has been withdrawn, and the union's regional secretary has said he will no longer speak at the event, even though it is to be addressed by the party general secretary, Iain McNicol, a former GMB official.

Miliband has said nothing about the controversy over Progress. But a Labour official said: "We are looking to attract new people to the party. The Labour party is a broad church and we are not in the business of excluding people."

Progress officials believe they face a campaign by unions to undermine them. They have been promised a meeting with officials from Miliband's office and McNicol to discuss their concerns.

The GMB motion argues that Progress has worked to promote its own parliamentary candidates and has been involved in pressing the Labour leadership to accept pay restraint and spending cuts.

One Progress official said: "It is true that 99.9% of the population have never heard of Progress, but they will hear [about it] if they think Labour is throwing out supporters of Tony Blair."

Senior members of the shadow cabinet criticised the union's move. One shadow cabinet source said: "In practice if they ban Progress, all they will be doing is closing down the Progress website, and they cannot do that. So what this is about is trying to bully people with the result that everytime a Progress member gets to speak at a party meeting they are denounced as disloyal."

Progress is not affiliated to the party in the same way as organisations such as the Fabian Society, so the conference could not order it to be disaffiliated, but it could be proscribed so that members would not be allowed to belong to the Labour party .

One Progress supporter said: "In some ways Miliband inadvertently let the genie out of the bottle by saying New Labour is dead. Well now he has to put the genie back in the bottle. It has got to be stopped."