‘Since 1992 it has again been possible to discuss without whispering the music of 1969-1976,” writes King Crimson’s Robert Fripp in the sleeve notes to the recently issued early-1970s live collection The Night Watch. “But I offer no apology for the transparently pratty music played by young dopes wearing satin.” Who does he mean, exactly? After all, though the current Crimson look like a fashionable firm of New York lawyers, they once epitomised the Tolkienesque fashions of the post-hippie era. But Fripp, 50 now, and the perfect softly spoken Dorset gentleman, won’t name names. “I’m loath to be drawn into making comments about other musicians, but I don’t think I was really part of the progressive scene,” he elaborates, “I was just playing music in that period.”

King Crimson began recording and touring again in 1994, to the delight of a hard core of fans big enough to fill the Albert Hall, but can they ever escape the stigma of progressive rock, with its Mellotron-toting, Tory-voting, tax-evading practitioners and their Page Three wives? Remember now and wince at Yes’s Tales From Topographic Oceans, at Emerson, Lake and Palmer, and at Rick Wakeman’s King Arthur and the Knights of the Round Table…on Ice. To add psychological credibility to the insane anti-hero of American Psycho, Bret Easton Ellis makes him a rabid fan of the Phil Collins-era Genesis, and the preface to Paul Stump’s recent and disarmingly frank history of Progressive Rock, The Music’s All That Matters, is defensively entitled Author “Not Mad” Shock.

But the cultural embargo on all things progressive increasingly smacks of hypocrisy. The post-punk history of the world ignores John Lydon’s love of Van Der Graaf Generator, accommodates prog’s more experimental German counterparts Can and Faust as “crazy dadaist Europeans”, and tolerates arrogant follies of U2 that are every bit as embarrassing as Yes at their most vain and absurd. The current critical favourites Spiritualised, playing alongside the English Chamber Orchestra at the Barbican last month, conjured up memories of Soft Machine’s big-band/art-rock fusion; and the much-lauded Radiohead’s more sublime moments sound like nothing so much as mid-1970s King Crimson. Just, from Radiohead’s album The Bends, lifts the guitar part of Crimson’s Red wholesale.

This week four current core members of King Crimson assemble incognito to offer four nights of live improvisations at Camden’s Jazz Cafe, under the moniker of Projekct One. A press release cites “expectations from audiences of established King Crimson repertoire” as a restric-tive factor in the band’s deve-lopment. Fripp has responded by forming Crimson “Projekcts” on both sides of the Atlantic, which he describes as “research and development fractals of King Crimson”, after a recent Polish tour, where he realised that not playing the 1970s hits to an audience for whom the ticket price would be a monumental expenditure, was simply unfair.

Such perversity has always been part of the Crimson working method. Asked how he plucked the drummer Bill Bruford from Yes in 1972, where his talents perhaps weren’t being exploited fully, Fripp diplomatically answers: “The muse descends on a group briefly, and takes them into its confidence and moves on, but time allows them to digest and apply the confidence that has been given. What usually happens is that the group tend to move towards obsolescence following success, and then droll repetition, whereas Crimson would take the information, deal with it, and then split up, as a response to the industry and the demands of its public. We break up, shake off all expectations and move on.”

In its three decades King Crimson has shed more expectations than a reasonably healthy snake might shed skins. Formed in 1969, their first four albums offered a baroque jazz rock, alternately hobbled by a pre-ELP Greg Lake singing Pete Sinfield’s sword-and-sorcery fantasy and sleazy groupie-sex lyrics and elevated by Fripp’s distinctive, restless guitar playing. The live quadruple CD Epitaph, issued earlier this year, “shows the 1969 Crimson was not this monolith of received wisdom”, says Fripp, “but actually a cracking little outfit for whom improvisation was a major part of what we did”. Appropriately, a 1970 edition of Top of the Pops saw the future 1970s superstar Greg Lake playing alongside the then unknown jazz pianist Keith Tippett on Catfood, Crimson’s sole hit single.

In 1972 a new Crimson, including the free jazz percussionist Jamie Muir, fresh from Derek Bailey and Evan Parker’s Music Improvisation Company, recorded a definitive triumvirate of albums culminating in Red, whose angular, uncompromising and occasionally quite terrifying music was often pasted together from the more inspired moments of live recordings. A leanness and economy, and a big improvisatory group sound, rather than strings of virtuoso solos, differentiated Crimson from their flashy contemporaries.

In 1981, Fripp re-formed Crimson again after a lengthy US sabbatical, with American vocalist Adrian Belew on board to free-associate about urban living over Bruford’s increasingly complex polyrhythms, the band abandon-ing their off-beat jazzy playing for a tight, machine precision derived from the New York No Wave symphonics of Glenn Branca and the minimalism of Steve Reich. “The vocabulary of rock music had changed,” Fripp offers, “and if you were a musician who was at all involved in speaking with the accent and dialect of the time to people listening at that time, you had to know that. The 1981-to-1984 Crimson had absorbed and noted some of these lessons and did not refer very much to the vocabulary of 1972 to 1974.”

So why reassemble Crimson in 1994? What has the band to offer now? How does Fripp know when the time is right? “How could you not know?” he splutters, breaking for the first time out of the considered calm that has hitherto characterised his answers. “You just know! When I met my wife I was a happy bachelor, and I proposed within a week. Why? Because she was my wife! I didn’t know this was Toyah Wilcox the star, because I’d been in America, but I instantly knew her as my wife. Likewise, when music appears that only King Crimson can play, King Crimson appears to play the music.”

Finally, Fripp breaks off – “to give my beautiful wife a kiss and a cuddle before she goes off to London” – and retires. “I’m looking forward to listening to Radiohead,” he says, genuinely curious. “I’ve just got back from the States and there’s a copy upstairs waiting for me.”

Projekct One play at London’s Jazz Cafe from tomorrow to Thursday.