Jeremy Corbyn is struggling to make his way to a cafe for a mid-morning break as he battles the after-effects of a cold brought on by a whirlwind six-week tour of Britain. Pushing his bike to the Grain Store restaurant at the back of King’s Cross station in London, the surprise frontrunner for the Labour leadership contest is stopped endlessly for selfies and by people who simply want to shake his hand.

Corbyn, who makes friendly conversation with every admirer, finally reaches the Grain Store, where he catches his breath only to have his hand shaken vigorously by the receptionist. “Mr Corbyn, you’re amazing. I have signed up to the Labour party just to vote for you.”

Pausing for a moment, Corbyn says: “I am just an ordinary person trying to do an ordinary job.”

Similar encounters across the country show how Corbyn’s world – and British politics – have been flipped upside-down by the surprise success of the veteran MP for Islington North who was barely recognised outside meetings of the Labour left until six weeks ago. Now he is on the verge of one of the greatest upsets in modern Labour history, which could see the backbencher beat the established party figures of Andy Burnham, Yvette Cooper and Liz Kendall to become leader of Her Majesty’s loyal opposition.

Why are young people rallying behind Jeremy Corbyn? – video Guardian

Town hall meetings for Corbyn are regularly packed out by Labour members, disaffected former voters and – yes – activists on the hard left who queue for hours to hear him explain how he would change the dynamics of Westminster by campaigning against the austerity of the Tories and ending the “austerity lite” approach of Ed Miliband. In a familiar sight at a rally in Norwich town centre on Thursday evening, Corbyn left the venue to address a crowd of patient supporters in the street outside after the hall quickly reached its capacity.

Corbyn, who only made it on to the leadership ballot in June with minutes to spare, admits that he had not anticipated the surge in support. “It has grown a lot faster than anyone could have understood or predicted or expected,” he tells me. “But it has shown there is such latent good, such latent enthusiasm, such latent optimism in people. This is a positive process. It is not negative. We are looking to do things rather than stop others doing things.”

Corbyn, who is 66 and was first elected to parliament in 1983, is an unlikely figure to lead a revolution. A tireless campaigner on the left on familiar issues such as Palestinian rights and civil liberties, Corbyn is no firebrand in the mould of a George Galloway. He makes no effort to change his dress habits of the past 30 years – pastel suits and a vest under his shirt even on a warm August day.

But his unspun approach – and clear lack of any media training in his television appearances – appears to be cutting through to new voters who are tired of the soundbites and perfect presentations of established figures. Corbyn invites contributions at his town hall meetings, though there was no mistaking the hand of the Unite trade union at his Norwich meetings as the union’s stewards policed the event. Official Labour party leaflets with details on how to sign up as a party member or registered supporter (membership is up 140,000 since the election) were handed out, showing how these packed rallies are potentially gifting Corbyn a massive bulk of voters in the leadership contest.

‘Let’s do hope not despair’: Owen Jones meets Jeremy Corbyn

He is adamant that the success of his campaign, while a surprise, is no accident and is part of a wider global surge from the left that has seen momentum grow for the socialist Vermont senator Bernie Sanders’s US presidential bid, Syriza’s success in Greece and the rapid growth in support for Podemos in Spain. “The mood is there and we happen to be in the middle of it,” he says. “We are not doing celebrity, personality, abusive politics – we are doing ideas. This is about hope. It is not just here. There are equivalent movements across Europe, the USA and elsewhere. It’s been bubbling for a long time.

“It is opposition to economic orthodoxy that leads us into austerity and cuts. But it is also a thirst for something more communal, more participative. That, to me, is what is interesting in this process.”

Corbyn has a message for Labour MPs who suggest that he would not have a mandate to lead the party after he made it on to the ballot papers when a group of his parliamentary colleagues, who profoundly disagree with him, “lent” him their votes to promote a debate. The support for him from beyond Westminster will represent a significant mandate in itself, he says.

Corbyn with anti-Pinochet demonstrators outside the House of Commons in 1998. Photograph: Fiona Hanson/PA

“I recognise that there are a lot of people that come together in this and want to take part in discussion and debate. It is a mandate.” With a twinkle in his eye, Corbyn says he is sure Labour MPs will appreciate how he has energised young voters. “I am sure the parliamentary Labour party will welcome this and understand it.”

A Corbyn leadership would represent a seismic shift for Labour in terms of how the party is led and in terms of policy. Gone would be the days of policy handed down by the leadership with little consultation. “There has to be an open debate in the party and so I have suggested we do a number of open conventions on the economy, the environment, the constitution, social and foreign policies,” he says.

The change in approach is causing heart palpitations among mainstream Labour figures, who fear that Corbyn would veer even further to the left than Michael Foot. The late Labour leader famously took the party to its worst result in 1983 since universal franchise on a manifesto that Gerald Kaufman famously described as the “longest suicide note in history”. On foreign policy, for example, Corbyn would vote to scrap Britain’s Trident nuclear weapons system and would seek to withdraw from Nato.

His language on Nato has not been heard from any frontbencher of either of the parties for three decades. “Nato was a cold war institution. It has given itself quite extraordinary powers of insisting on 2% defence expenditure of all its member states.”

Corbyn has been accused of failing to see the threat posed by the aggression of Russian president Vladimir Putin, but he makes clear that he is highly critical of him. “I am not an admirer or supporter of Putin’s foreign policy, or of Russian or anybody’s else’s expansion. But there has got to be some serious discussions about de-escalating the military crisis in central Europe. Nato expansion and Russian expansion – one leads to the other, and one reflects the other.

Corbyn makes clear that it would be wrong to allow Ukraine, as a divided country, to join Nato. “To recruit into membership a divided country means you either accept the division or you intend to do something about it. That is dangerous.”

Corbyn even suggests it was wrong to allow countries such as Poland, as a former member of the Warsaw Pact in the Soviet orbit, to join Nato. Asked whether it was a mistake to admit former Warsaw Pact countries, he says: “I think it probably was, actually. We should have gone down the road Ukraine went down in 1990, which was an informal agreement with Russia that Ukraine would be a non-nuclear state [and] would be non-aligned in its foreign policy. The interesting thing is why Russia didn’t turn all that into a treaty, why they just accepted it as an informal agreement with Nato, the EU and the US.”

It is not just Corbyn’s approach on foreign policy that is causing alarm among established party figures, a panic highlighted by the call this week from the former home secretary Alan Johnson for the Labour party to end the madness and vote for Yvette Cooper. A proposal for “a people’s quantitative easing”, to fund a national investment bank to boost house-building and other areas, prompted claims that Corbyn risks stoking inflation. He says this is wrong because of uneven economic growth and low wages outside London.

“The economy is growing very unevenly on a regional basis, where wage levels are significantly lower in the east Midlands and the north-east compared to London and the south-east. In turn, it is growing unevenly because of unequal investments in infrastructure.”

In a message to those who claim his economic approach is a throwback to Labour’s profligate days of the 1980s, Corbyn says he is committed to eliminating the current budget deficit. “Yes we do,” he says of a desire to tackle the deficit. But he adds: “Don’t set an arbitrary date to do it. The idea that we are some kind of obscure deficit denier is a total nonsense. Why is Joseph Stiglitz welcoming what we are saying? I think we have already changed the economic debate in Britain.”

To those Tories who hope to depict Corbyn as a politician who would like to raise taxes “until the pips squeak”, he says his plans are modest on that front. He would restore the 50p top rate of income tax and stop George Osborne’s cuts to corporation tax. On his plan to cut corporation tax, he says: “You end up with a corporate free-for-all in which we are all playing catch-up with big corporations. There needs to be some kind of collective agreement on minimal levels.”

Corbyn and supporters as he launches his policies for the environment this week. Photograph: See Li/Demotix/Corbis

Corbyn is offering words of assurance to his party, and yet senior Labour figures have grave fears that his leadership could take them into the electoral wilderness. These doubts have surfaced in public after party figures raised concerns about “entryism” in the leadership contest, as it revealed the names of known activists on the hard left who have signed up to take part in the leadership contest.

A veteran of the battles of the 1980s, who in the eyes of his critics failed to confront the Militant Tendency, Corbyn said he warned of the dangers of the new system from the outset. But he believes that only a small number of people are seeking to disrupt the contest. “The numbers don’t stack up,” he says. “The entryism, if anything, is of enthusiastic young people. We can all be happy about that.”

The Corbyn bandwagon represents no coup, he says, as he jokes that people should set aside their copies of Chris Mullin’s novel A Very British Coup. This tells the story of a leftwing British prime minister, Harry Perkins, who loses power as the establishment and the US take fright.

“Do I look like Harry Perkins?” he jokes as he looks across to St Pancras station, where the prime minister arrives on a train from Sheffield in the film version. “This is a bit of an open coup because there are thousands of young people joining in. There is no coup here, there is no capture here. This is popular debate and popular discussion.”

As reassurance to nervous people in Labour, Corbyn chooses an unlikely candidate as the party leader he admires most. This is the cautious and establishment figure of John Smith, who listened to Corbyn’s opposition to a welfare report for two hours even though he did not support him in the 1992 leadership contest. “What a decent, nice, inclusive leader he was. What a tragedy he died when he did.”

To the likely disappointment of his opponents, Corbyn does not even mention Foot in his pantheon of former Labour leaders, though he held him in great esteem. “Michael and I were very close and very good friends,” he said when asked why he had omitted the man who was leader when Corbyn was elected to parliament for the first time. “I liked Michael a great deal. I only came into parliament after the 1983 election. It was a very depressing period for the party, and I admired the way Michael stayed on as the interim leader until the autumn. It must have been a very tortuous summer for him.”