Maggie Dunn has worked with Jeremy Corbyn since the Winter of Discontent in 1978-79, when they were both officials at Nupe, the now-defunct National Union of Public Employees. She is one of his oldest political friends. On Friday she took a break from the Corbyn for Leader campaign and headed to the Buxton opera festival in Derbyshire.

“It is all very exciting,” says Dunn, who can’t quite believe how, after all the years of singing old tunes that few wanted to hear, Corbynism is now resonating up and down the country with young and old. In Buxton she found herself discussing plans to take state services back under public ownership with a clerk from the House of Commons.

“It does feel unreal. I am having political discussions that I haven’t had for donkey’s years. People are talking about whether we should be renationalising things. It is wonderful.”

She has a grandson at Oxford University who tells her that Corbynism is catching on there, too. “He says they are all wearing Corbyn-for-PM T-shirts. They are struggling to pay for their books and coming out of university with huge debts and here is someone saying he wants a completely different society.”

Just as the MP for Islington North’s appeal in the contest for the Labour leadership has surprised and shocked much of his own party, it has stunned the Corbyn campaign itself. It is struggling to keep up, and to deploy the many resources it now has at its disposal to maximum effect. Kat Fletcher, who is running a team of volunteers (more than 4,800 have signed up online in the past few weeks) says the momentum is unstoppable. A series of polls have put Corbyn within striking distance of victory against Andy Burnham, Yvette Cooper and Liz Kendall, and a sense that something that seemed unthinkable a few weeks ago might be about to happen is feeding the frenzy.

“It is completely overwhelming. When I first joined a few weeks ago, it was extraordinary and it is not slowing down. Every morning I open my inbox and go ‘Wow!’. The phone never stops ringing, and the emails never stop coming in.”

The campaign now has two HQs in central London: one in the offices of the Unite union, where Fletcher works organising volunteers – from an “elderly gentleman” who writes thank-you letters to donors to young people wanting to run street stalls selling “Jez We Can” T-shirts at £10 a time – and another at the base of the TSSA union, where the press operation is based.

New offices and phone banks are being set up by the day. This week a huge Corbyn phone bank will be established in Liverpool, with 100 or so phone lines, from which volunteers will ring Labour party members and urge them to register so they can vote Corbyn when ballot papers go out on 14 August. They pump out material on Twitter and Facebook – outlets that were pretty marginal for Corbyn until recently.

Corbyn, left, with fellow candidates Yvette Cooper, Andy Burnham and Liz Kendall with journalist Paul Waugh (centre), at a Labour hustings event in Warrington on 25 July. Photograph: Paul Ellis/AFP/Getty Images

Carmel Brown, a Team Corbyn press officer and a veteran of the Stop the War and anti-poll tax movements, asks what has generated all this momentum and in the same breath answers that Corbyn is not from the Westminster bubble. “You have to look right, dress right, sound right, slick, slick, shiny, slick … Jeremy does none of those things. Everything on the inside that people talk about in the bubble and all the jargon, nobody in the outside world gives a damn about.”

They don’t understand the nuanced messages and triangulations of the other candidates. “People talk about the race to the bottom,” she says furrowing her brow to show incomprehension. “It means nothing. Jeremy is not like that. This is like Stop the War with bells on.”

Lynn Hemming, a housing support worker from Lancashire who has volunteered for the campaign, says Corbyn has always been consistent and can be trusted. It doesn’t matter that the policies are from a bygone era. “I believe you can trust in what he says. I wasn’t tempted to support any of the other candidates, although my second choice would be Yvette Cooper. I don’t understand why Liz Kendall is even in the Labour party. Jeremy Corbyn is saying things that haven’t been said for a long time – policies you can get your teeth into. He’s thinking practically about people and jobs.”

Helen Kreissl, 37, an administrator at the University of Manchester, is among thousands who have signed up for Labour membership so as to have a vote, motivated by having the Corbyn option. “Finally, someone with the passion and principles we need,” she says.

Team Corbyn has Simon Fletcher, who worked as Ed Miliband’s link man with the unions, on board. They present their candidate as straight-talking, clear, and principled. One issue they have struggled to be clear about, though, is his attitude to UK membership of the EU. In hustings, Corbyn has equivocated, not saying whether, as leader, he would campaign for the UK to stay in. Asked to clarify his position on Saturday, he steered more towards the “in” line, saying that Labour should argue for a better EU. “That does not mean walking away, but staying to fight together for a better Europe.”

From the centre and right of the Labour party, opponents have tried using scare tactics about Corbyn. Last week Tony Blair said people who had set their hearts on him needed to “get a transplant”. Margaret Beckett declared she had been a “moron” to nominate him as now he stood a chance of winning. Donors have said he will drive them away and others say he will split the party if he wins. But the “beware Corbyn” tactics have not worked.

On Saturday, deputy leadership candidate Angela Eagle, writing in the Daily Mirror, urged people to “lay off” Corbyn because the attempts to portray him as representing the end of Labour as we know it were backfiring. “The unwelcome briefings and public prophecies of doom and destruction from senior figures are doing more damage to the party than they are to the leadership candidate himself.”

Corbyn’s old friend Dunn says she expected the media to tear in to him as an ageing, bearded leftie with prehistoric views who was unelectable. Instead he has become the story, and it’s the other candidates that have seemed tired, dreary and old. To her surprise, Corbyn has somehow become the new phenomenon in British politics, preaching policies largely unaltered in 40 years. “It is extraordinary when you go to meetings with him,” she says. “A 66-year-old white male who is treated like a rock star.”

‘Honesty is very compelling’: Corbyn supporters speak

Lola May, 17, sixth-former, from London: “I feel like the Labour party has forgotten it is supposed to be socialist. I didn’t like it when Miliband supported austerity and, although I wanted them to win the election, I didn’t like his rhetoric on immigration either. This leadership campaign is so important, and I think Jeremy Corbyn stands out, on anti-austerity, on education, on a platform of wanting to help young people and the vulnerable. I want to go to university and to be able to get a job, so I guess I might be being selfish in wanting things that are beneficial to me, but I think what he is saying would be beneficial to everyone. People have to understand that politics is so relevant to everything and get far more passionate about it.”

James Schneider, 28, writer, from London: “I joined the Labour party just after the election and before Jeremy Corbyn was on the ballot paper for the leadership. I had been very disappointed with the way Labour ran their election campaign – the whole thing was miserable. Corbyn has re-energised people and he has done it mainly through good arguments. I don’t agree with everything he says. Those who claim to know about politics and who are conditioned by the politics of the past 20 years say he couldn’t become leader, but I think a person who says what he means and means what he says is exactly what people want. Honesty is very compelling, and has crossover appeal.”

Will Armston-Sheret, 20, history student, from Hampshire: “This is the first opportunity for my generation to have a say in creating a genuine leftwing Labour party. Corbyn is one of the very few politicians in a long time to be clear about what he believes in and to be genuine leftwing Labour. I think he could be prime minister – it’s hard to speculate on that because even if he doesn’t, he is one of the few politicians around for a long time who thinks beyond the present, and that’s a great draw. I think Labour needs to really stand up and properly oppose for once – there’s no point in winning power if you’ve sold out long before the election.”

Jayne Hardy, fitness instructor, from Manchester: “I have just registered my support and will be voting for Jeremy Corbyn for Labour leader. Well done to him for sticking up for ordinary people. I don’t actually care if this creates a rift in the Labour party – if he is elected he will be the shake-up Labour need to get their arse into gear and make them re-evaluate themselves. The Labour party have been hiding in the shadows and cowering in fear. It’s time to come out guns blazing.”

Omar Laftah, 34, from Stoke-on-Trent: “Jeremy Corbyn deserves to be elected and I cannot understand how anyone who is in the Labour party now can’t see that. The other three candidates won’t do anything to solve this problem we have. We need people with solid old Labour principles and values, like Corbyn and Dennis Skinner. Corbyn talks about how to go to battle with the Tories, how the bankers have got away with so much and also the tax avoiders. We need a strong leader who has great experience to deal with these problems. Corbyn is the man who can bring this party back to some credibility, because under Ed Miliband our policies just were not good enough.”