It was an inauspicious start to one of Britain’s most enduring – and enduringly successful – bands. “We met when Jeremy was trying to get off with my girlfriend in a pub in Brighton,” says Mark Chadwick, singer and guitarist of folk-punk group the Levellers.

“I was just sitting there talking to her,” picks up bassist Jeremy Cunningham, “and then he came in, and I was like, ‘Oh, fuck, he’s much better looking than me.’ But then we got to talking about music, didn’t we?”

It turned out that both men were in bands, and neither was happy about those bands’ failure to sing about anything important. Chadwick told his new buddy he’d written some songs that were more along the lines of what they were talking about. “So I went round his place and played them for him.”

“I was blown away,” Cunningham says. “We still play a couple of ’em now.”

This year, the Levellers’ celebrate 30 years together, marking the occasion with an acoustic album, We the Collective, of eight old songs and two new ones. For much of that time they have been resoundingly unfashionable: if you judged a group’s success by press coverage and radio play, you would assume the six-piece were these days plying their trade to half a dozen diehards in pub backrooms. In fact, every year they sell all 17,500 tickets to their own festival – the proudly sponsorship-free and affordable Beautiful Days, in Devon – and have notched up seven Top 40 albums and 14 Top 40 singles.

There was a period when the Levellers were the most popular indie band in Britain – their 1994 performance at Glastonbury was reckoned to have drawn the biggest crowd the festival had seen. They embodied the subculture known mockingly as “crusty” – the travellers and punks and social outcasts who were scoffed at for their dreadlocks (Cunningham remains extravagantly belocked) and for their dogs on strings. “There were lot of disenfranchised people,” Chadwick says. “They were pissed off and we were talking to them. Instead of talking about drugs and girls, we were talking about their lives.”

The Levellers in 1995 Photograph: Martyn Goodacre/Getty Images

The contempt of the press irritated the Levellers. They accept that many music writers just didn’t like the music. But they also think their image didn’t fit in with received notions of cool. When one NME critic gave their 1991 album Levelling the Land a kicking, Cunningham responded – prefiguring Sharon Osbourne – by sending him a piece of human excrement. “It was in a shoebox, nicely gift-wrapped. It’s not one of my proudest moments.”

The crustiness meant the Levellers had a puritanical image (“People thought we were out selling Socialist Worker or something,” Cunningham says) but at the peak of their success, they were prone to just as much ridiculous rock-star behaviour as any other band in sudden possession of money and surrounded by people keen to indulge them – the drugs, the drink, and the cliche of the television and the hotel window. “It was an A&R man who wanted to throw the telly out of the window,” recalls Chadwick.

“But he didn’t have the bottle to do it.” Cunningham chips in.

So Chadwick took charge, ripping the TV from the wall, pulling out the cabling and dispensing the lot on to the street below. “I had a shower, got into bed,” Chadwick recalls. “Next thing I knew I had a torch in my eyes and it was the Met, saying, ‘Come on, sonny.’ There’d been a guy in a telephone box who’d phoned the police. But he never showed up as a witness, so I got away with it.”

On stage at Brighton’s Corcorde 2 in May 2002. Photograph: Ian Dickson/Redferns

The Levellers, by their own admission, were a creation of Margaret Thatcher. Not just in the politics of the 1980s giving them the pricks against which to kick, but in the funding they got to run the band through the enterprise allowance scheme (“Though we did abuse it,” Cunningham admits). They say their songs aren’t polemics – though the new album contains a cover of Subvert by the 80s anarcho-punk band Zounds – but reflections of real life.

They’ve tried to retain their principles – they once turned down £250,000 to headline the Reading festival because they despised its commercialism – and Chadwick says that the thing he values most is their connection with their fans, and the fact they remain approachable (“If they come to the local pub, they can have a pint with us”). He’s happy to take on those among his audience who want to argue the case for the opposition. “You’d be surprised how many Tories and Brexiteers like the Levellers,” he says. “And I will rag them and rag them until they cry. Or until they never come to see the band again. But I don’t care.”

All of which makes the fact that the Conservatives once approached Chadwick to stand as a councillor for Kemptown in Brighton all the more surprising. “I said, ‘Are you insane?’ It was because I had a profile and I was political.” The Greens, Liberal Democrats and Labour have also all approached him, and he has said no to them all, though last year he joined the Labour party, “because I could see something different there, something positive”.

After 30 years together, Chadwick and Cunningham sound like nothing so much as the two old codgers who’ve spent most of their lives propped up at the bar, noting the injustices of the world. “If we could get get away with doing nothing, we probably would,” Chadwick. “We’re not that driven. We were once, but you can only be like that for a certain amount of time before you realise it’s pointless if you want to live a life, rather than drive a life.”

And they still have their heroes. All the Levellers were inspired as young people by Crass, the punk band who lived as a collective in a farmhouse in Essex (“The only thing that was unlistenable was the music,” Cunningham says). Years later, they booked the band’s frontman Penny Rimbaud to play at Beautiful Days. “I told him, ‘If it wasn’t for you, none of this would be here.’ He said ‘You’re the fourth member of your band that’s come up to me and said that.’”

Chadwick recounts his own memory of meeting a hero. “I did the same with Johnny Cash.”

“And what did he say?”

Chadwick adopts a burly deep-south baritone. “He said, I’m not familiar with your work, son.”

And the two of them hoot, fit to burst.