They may be fortysomething family men nowadays, but get them together and Madness are still the Bash Street Kids of Britpop. Formed in Camden Town 30 years ago, these cockney chart veterans clearly function as much like a gang as a band. Even with wives and grown-up children in tow, the chemistry between them is instantly that of the school playground. Impenetrable in-jokes and affectionate insults abound.

With a new album and a December arena tour in the offing, Madness are back in business. After a summer playing continental festivals, including unbilled, roof-raising sets at Glastonbury and Bestival, they are now recording their first new material in a decade. An album is tentatively scheduled for next year.

“An album that we started recording in 1947,” deadpans the singer Graham “Suggs” McPherson, “it should be out in 2019.” McPherson’s co-frontman Carl “Chas Smash” Smyth adds, with no apparent irony, “It’s going to be our Sergeant Pepper’s”.

Madness do not even currently have a record deal, but they insist such trifling details scarcely matter in the download age. Like dozens of established pop brands, from Radiohead to Marillion, the Nutty Boys have realised they can function outside old-fashioned record industry rules. Their ambitious new manager, Gary Blackburn, has even hinted that the new album could be given away with a newspaper, following Prince’s example.

“A lot of boundaries seem to have broken,” says the Madness founder and keyboard player Mike Barson.

“Because the whole business is changing, it’s about how you utilise that energy. Prince giving away his album would have been incomprehensible a few years ago. But that’s just another way of doing it.”

More than three decades into their career, Madness have just finished one of their busiest years playing all across Europe. With their strong live reputation, the proliferation of festivals aimed at older crowds with young children has provided them with a fresh pool of fans and a lucrative new business model.

“These festivals are a revelation to us,” Suggs says. “We’re playing places we didn’t even play when we were in our pomp. Like in France, 60,000 people went f***ing bananas. When they see Madness they see something they have never seen before. We’re not Arctic Monkeys, we’re not the Rolling Stones, but we’re not The X Factor either. Somewhere in that grey area, outside the norms of the music business, Madness exist.”

Being in Madness in 2007 is obviously a family affair. The aftershow party for their London date in December will include a performance by Deaf School, the band fronted by McPherson’s wife Bette Bright, plus a “battle of the organs” between Barson and his son Tim. DJ duties will be handled by Smyth’s son Casper and McPherson’s daughters, Scarlett and Viva.

“Madness is a surrogate family,” Smyth says. “It’s a question of co-dependency and dysfunctionality. Our families of origin are dysfunctional, so we came together looking for some sort of family substitute. All art is based on neurosis, isn’t it?”

A uniquely London blend of story-telling lyrics, Jamaican ska rhythms and music-hall nostalgia, Madness are a much-loved English institution. But Englishness can be a loaded term. In the late 1970s they attracted a small but vocal following of violent, racist skinheads. An initial reluctance to condemn National Front fans outright led to press speculation that the band harboured racist sympathies themselves, an absurd slur given their long history of working with black musicians and celebrating Jamaican music. Almost three decades later, the accusation still rankles.

“You would need a whole book to write about those times,” Suggs sighs. “We were in the thick of something no one will ever see again, I hope. But so were a lot of bands. They were clamping down on football hooligans, so all the hooligans were aligning themselves to bands. That whole era was very violent and mad, and we were right in the middle of it.”

But mud sticks, of course. Suggs suspects Madness are still dogged by their early association with fascist thugs. “To be perfectly frank, the reason they didn’t really want us at Glastonbury was because of that worry, so they let us on secretly,” the singer says. “But it was 20 or 30 years ago! The lucky thing for us was, at the turning point in Britain between the 1970s and 1980s, those f***ers went on to Oi and hardcore punk. Praise the lord, we were just seen as pop lightweights, not standing up for our nation. They left us behind.”

Madness enjoyed a dazzling run of chart success in the early 1980s with bouncy singalong hits including Baggy Trousers, House of Fun and Embarrassment. Like some kind of cockney Abba, their later singles became increasingly wistful and bittersweet. Behind the cartoonish Nutty Boys image, all was not well.

The band disintegrated in the mid1980s when Barson departed for Holland to spend more time with his Dutch wife Sandra. They eventually reformed for the first of their mammoth “Madstock” weekends in Finsbury Park, London, in 1992, which was initially intended to be a one-off. The shows were sell-out successes, causing frenzied dancing among the crowd that triggered a seismic tremor measuring 4.5 on the Richter scale.

Regular reunion tours followed, culminating in a new studio album in 1999, Wonderful. An award-winning West End musical based on their songs, Our House, and a 2005 album of ska covers, The Dangermen Sessions, further established the band as an evergreen musical institution.

“We look back on when we stopped as the right decision, but executed the wrong way,” Smyth says. “We should have just let everyone take a rest and then come back together again, because that’s what’s happened since then. Since Mad-stock in 1992, we only do things when it feels right. We have that luxury.”

A lot of troubled water has passed under the bridge during their 30 years, but Madness have outlasted countless fall-outs and break-ups. Barson is divorced, and divides his time between Britain and Holland. Suggs has a high-profile career as a radio and TV personality, and can currently be seen singing in a fish finger advert. Even so, the old teenage gang mentality that first drew them together keeps calling them all back.

“I could be doing something every day of the week outside the band,” Suggs nods. “But ultimately, this is my favourite of all the things I do. We’re old mates, you know? It’s love and hate and all those other things. I’ve done solo records, but you’re never going to get an outfit like this, whatever money you pay.”

Suggs likens Madness in 2007 to former boxing champs training to get back in the ring. But their rapturous reception at Glastonbury and Bestival suggests the band’s populist punch remains as strong as ever, even as they approach 50. Conditions certainly seem healthy for a full-blooded comeback. The shifting goal-posts of record industry power have given the band a new lease of life.

“Madness is a very bizarre thing,” Suggs says. “Something is happening recently to do with our legacy in terms of what people feel about us. Like going to Glastonbury, doing it for no money, on a secret stage – but we knew we were going to blow the roof off the place. Without being big-headed, that is our legacy.”

Madness’s tour opens at the P&J Arena, Aberdeen (www.madness.co.uk0870 1690100), on Dec 6; a single, NW5, is out on Dec 17 (Lucky 7 Records)

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