Located in a shabby portacabin off Hayes high street, everything about John McDonnell's offices says Old Labour. Union flags and banners decorate the windows and walls and various trade union awards and trinkets occupy a cabinet, which is the only piece of furniture in the waiting room save some fold-up chairs – even the carpet is red. This a fitting environment for McDonnell, who cut his political teeth as a researcher at the NUM, before going on to work for the TUC and then as Ken Livingstone's deputy at the GLC – before being fired for being too radical for "red Ken".

After 1997, McDonnell voted against almost all of New Labour's flagship policies, including the war on Iraq, foundation hospitals, top-up fees, trust schools and anti-terror laws - "it wasn't an oppositionist position – I was opposing things because they were just wrong. I couldn't do anything else, there was no compromise." He stood for the party leadership once, after Tony Blair stood down in 2007, and again in 2010 – both times on the promise that he would reverse the party's moves towards privatisation and reinstate a "real Labour government". Despite support from the TUC and party members, he twice failed to receive sufficient nominations from MPs to go through to the electoral college stage.

He is keen to stress that he never intended to stand for leadership, saying he only did so in order that the left of the party could "publish a political programme and demonstrate we've got support for that political programme". He says that the high bar for parliamentary Labour nominations meant "I was blocked from the ballot paper They were terrified that if I got on the ballot paper I would show sufficient breadth of support from the rank and file members and the trade union movement that they'd have to acknowledge there was support for the policies I was advocating." Who is this "they"? "Blair and Brown, that whole clique basically."

Why, then, did he stay with Labour, when its leaders were advocating policies to which he was morally opposed? "Because it's my party, not theirs. I saw the Blair-Mandelson regime as a coup, and I think it was a well-funded coup as well – resources obviously came from big private-sector backers. But all through that period the bulk of the rank and file party were what the party has always been, a socialist party."

And what about now? McDonnell suggests that Labour Party supporters are moving away from what was "the march to the neo-liberal right" - "A lot of people woke up and thought 'how have we got in to this?'". He said that Labour's opposition to the coalition's welfare uprating bill was demonstrative of a "significant shift in parliamentary Labour Party attitude". "The debate was tremendous – Labour MP after Labour MP getting up and putting forward the arguments about deprivation and redistribution of wealth." Equally, he says, Ed Miliband's recent policy proposal to bring back the 10p tax rate funded by a "mansion tax" is another sign of a shift to the left - "it recognises the mistake it was to abolish it but also more importantly it is part of the process of reasserting the role Labour has to play in redistributing wealth."

For McDonnell, who chairs various socialist groups, including the Labour Representation Committee, the Socialist Campaign Group and Public Services Not Private Profit – the left of Labour is regaining power within the party. This is aided greatly, he says, by the development of new media. "In the past the media was a real problem. In terms of mainstream media it's very difficult to break through if you're on the left." An exception to this rule is Chavs author Owen Jones, who previously worked for McDonnell organising his leadership campaign. "Owen's done very well, he's been swept up, and it's a real breakthrough – he's done fantastically" - although McDonnell fears "they'll do a token lefty and make or break”. Who is the 'they' in this case? "Just the establishment, the establishment. But it doesn't matter because we create our own media – new technology has given us blogs, it's given us Twitter. Public meetings are packed these days".

For McDonnell, the role of Labour's left is now to make issues "safe" for the party's leadership. "If you make an issue safe, Ed Miliband will shift. Whether it's Murdoch, banks, welfare or benefits But I don't think they'll just shift cynically, they'll shift on to the terrain that is then safe, and you can have a proper discussion then." As an example of this process, he cites the treatment of people with disabilities who were subjected to the Work Capability Assessment, a process that was initiated by New Labour and built upon by the coalition, who enlisted private IT firm Atos to finish the job. "We had two years of arguing and demonstrating how bad it was and got nowhere. In fact it was almost physical in the chamber at times – you felt threatened. But now we've got a whole swathe of opinion within the Parliamentary Labour Party and now we've now got the frontbench standing up and criticising Atos as well." He also cites the black-listing of trade union members in the construction trade as another example of an issue that's been made "safe" - "we've now even got Chuka Umunna jumping up and down about it."

McDonnell, an anti-capitalist who subscribes to a Marxist conception of class, last year published a "Radical Alternative to Austerity" in which he detailed his vision of a "democratised economy", with public ownership of firms and the City, a tax on financial transactions and a 60 per cent rate of income tax on earnings over £100,000. He concedes that he'd have a much harder job trying to get the Labour frontbench to commit to this kind of socialist policy. "The Labour leadership comes from a neo-liberal background. They served their apprenticeship deep in the heart of New Labour and they're looking to come back as New Labour mark two, slightly reformed but not challenging the system itself."

But he says that as the economic crisis deepens they'll be "forced to look at more radical options". Talking about his own constituency Hayes and Harlington, for which he has been MP since 1997, he says "we have an open-door policy four days a week because people have so many problems. I've got people coming in who are close to eviction, can't afford to pay their rent, under incredible stress – all that stuff about parents choosing between heating and eating happens on a daily basis."

He tells me that he thinks the left of Labour is even beginning to make headway on radical reform. "It's beginning to move, even there, we've got a situation where the party is looking back again to its roots around cooperation. It's beginning to open up. So what I want to do is make safe the debate around systemic change." There's a small pause before he bursts out laughing. "It's ambitious," I say.