Jeremy Corbyn called on festivalgoers at Labour Live to unite to take on inequality and deliver a Labour government to replace a party that is “incapable of governing” in a rousing speech reminiscent of his appearance at Glastonbury last year.

Labour supporters gathered in north London on Saturday afternoon for a music and politics event also known as the JezFest, which was attended by around 13,000 people at the White Hart Lane recreational ground.

Corbyn was introduced by John McDonnell, who came on stage after a rendition of All You Need is Love, and gave a five-minute speech where he referred to The Magic Numbers who had preceded him with a solid set and pledged that a Labour government would be magical.

“I had a dream we’d have a socialist in No 10 and it’ll be this socialist, Jeremy Corbyn!” he said, before giving way to the party leader.

Corbyn then arrived to cries of “Oh, Jeremy Corbyn” and gave a 25-minute speech where he criticised an economy and a society ruled by the free market.

“The legacy of the next Labour government will be a national and education service that takes the commodity out of education,” he said.

“Under Labour mail, rail and water will come back where they belong into public ownership,” he said. “It will be democratic and it will be well run.”

In a speech highly critical of the Tory government he said: “I look in the House of Commons, across the aisle, at a party of the rich, by the rich, for the rich and funded by the rich and I see a party over there that’s divided, incapable of negotiating and incapable of governing.

“I see a party that offers nothing to bring about the necessary solutions to people’s problems in our society and I simply say to them this: you crept back into office a year ago ... for goodness sake, give up, move on, move over and let the people take over,” Corbyn told the crowd before introducing Reverend and the Makers, who he had introduced in Tranmere last year when the famous chant was born.

A diverse group of people young and old, black and white, middle and working class wandered across the grass between stages throughout the day, as the crowd steadily grew in number.

The tents were packed throughout the day, which had intervals of sunshine, although the music was relatively less well attended.

The MP and former trade unionist Ian Lavery got a good turnout in the Solidarity tent, along with Dan Carden MP and Len McCluskey for the People’s Question Time.

The Literary tent was packed for the Guardian columnist Dawn Foster and editor-at-large, Gary Younge, who talked about how a new generation of Labour voters was interested in bringing the party back to its roots following the 2015 defeat.

At the Socialist Bookmarks shop, books on offer included Unravelling Capitalism, the Rebel’s Guide to Gramsci and the Ragged-Trousered Philanthropist.

Contemporary leftwing authors were close by, preparing to speak.

People have been … disengaged in politics and one party is trying to appeal in a different way Alex Nunns, author

“Given the overwhleming onslaught of sneeriness, snideness, snarkiness and snobbery about this event from opponents of Jeremy Corbyn, it’s just nice to actually be here and see there’s a whole bunch of people having a nice time,” said Alex Nunns, the author of The Candidate: Jeremy Corbyn’s Improbable Path to Power.

“We live in a country where people have been completely disengaged in politics and one party is trying to appeal in a different way and make it a little less dry.”

The failure to sell out Labour Live might be evidence of a labouring love for Corbyn’s brand of socialism, but the cult of personality endured among the faithful on an overcast day.

Tony Lennon, a retired stage manager from Shropshire, was unconcerned about the initial poor turnout. “It’s not about making money,” he said. “It’s about bringing people who believe in the same sort of thing together. If this is the first time they’ve organised a festival like this, then they’ve done really well. Weather’s not so good, but I think overall it will do the job.”

The People’s Question Time in the Solidarity tent. Photograph: Rick Findler/PA

Festivalgoers appeared most concerned about education, housing, wages and the NHS rather than Brexit. The mostly remain voters rued the “disaster of leaving the EU”, but said the referendum result must be accepted and it was not among the top of their priorities.

“The debate is dominated by pedantic squabbles,” said Chris Saltmarsh, a 22-year-old climate-change campaigner from Liverpool. “There are many more important things for the political elite to worry about.”

As the Guardian columnist Owen Jones took to the main stage and restated Labour’s pledge to abolish tuition fees, renationalise industries that “belong to us” and give people a proper living wage to whoops from the crowd, there was a palpable feeling that Corbyn was plugging the right line – to the diehards.

Labour Live at White Hart Lane recreation ground. Photograph: Andy Hall/The Observer

A Labour party spokesperson said: “Labour Live has been a fantastic day. We’ve brought people together from all walks of life to have a good time to enjoy the acts and family entertainment, and discuss how we can change our society for the better.

“The tents have been packed all day and there has been a great atmosphere. This is the first event of its kind organised by a political party, and we have demonstrated how politics can be opened up to a wider audience and to people who have been shut out for far too long.”