Live at the Roxy London WC2 (Jan-Apr 77), one of punk's indispensable artefacts, begins much as you'd expect, with three tracks of phlegm-flecked mindlessness from Slaughter & The Dogs and The Unwanted - bands as boneheaded as their names. Then there's a drawling voice, gentle but insistent: "Pay attention ... we're Wire." The tone is of advice rather than demand, and rather fails to register. The band lurch into the low-fi drone of ‘Lowdown', restarting every time they seem about to stop: "Another cigarette / Another day / From A to B / Again avoiding C, D and E." Finally, they grind to a halt, almost arbitrarily, amid uncomprehending silence. No applause. No cheers. Somewhere, a bottle can be heard smashing.

The attention has been a long time coming. Last month, 150 bands strutted seven stages over two days in Hainault Forest, near London, during the sprawling Offset Festival, a showcase mainly for young hipsters like The Maccabees and The Young Knives. Top of the bill were Wire, with a new album to spruik, Object 47. Covered over the years by performers from REM and Henry Rollins to fIREHOSE and the New Bomb Turks, they now find themselves being name-checked by bands whose members were not even born at Wire's 1985 reunion, let alone their 1977 inception. For long-term fans, it's a slightly odd feeling, like being a lifelong lover of quilting, then learning that Paris Hilton is to base a reality-television show on her new besottedness with appliqué.

Object 47, so named for being the forty-seventh item in Wire's catalogue, is disarmingly smooth and fluid; a compact, melodic, egg-headed 35 minutes, with lyrics full of bleak, dry humour. Which invites a musing: how many bands 31 years after their first recordings are bothering with new material, new directions, and so obviously aiming primarily to satisfy themselves in the process? For unlike the host of 1970s bands revived by their members for superannuation purposes, Wire still play like they mean you to pay attention.

The night I saw Wire on a flying visit to Melbourne's Corner Hotel, a few years ago, started wretchedly. I arrived with a friend during the performance of a support band so self-consciously apathetic that I couldn't be bothered learning their names - lucky for them. Wire then took the stage, somewhat inauspiciously, the four members in their fifties and looking it. Vocalist Colin Newman could have been an academic from a Malcolm Bradbury novel; guitarist Bruce Gilbert so resembled the English tourist of imagination that he should have been wearing one of those zip-up moneybags around his waist. To be sure, you'd have avoided burly bass player Graham Lewis if you'd glimpsed him on the Tube, imagining him on the way to manning a door at a nightclub; but drummer Robert Grey (AKA Robert Gotobed) would have looked more at home pottering round his vegetable garden. So, there they were: Wire. If they'd turned up for karaoke, you'd have been embarrassed for them.

The night remains one of the most cherished memories of my music-going life. Wire burst into tracks from their latest release, Send (2003), whose power-packed rhythms took the band's sound to the brink of techno, and absolutely nailed them. Newman commanded the stage with a kind of owlish charisma; the sonic wallop of Gilbert's guitar reverberated off the walls. After three songs, my friend and I exchanged excited glances. They were good. They were so good. In the second half of the set, Wire started picking at random from their first three albums, Pink Flag, Chairs Missing and 154. Nor were these easy-listening singalongs for the fans, but big, beaty, pumped-up and punked-up, as though the songs had been written the week before, not during the Queen's Silver Jubilee. It was only as the band members sloped off the stage that they looked a little senior for all this excitement, ready for bed and a Horlicks. The mood in the audience was not just ecstatic but validated. I bought a T-shirt, which when it quickly disintegrated was converted by an artful girlfriend into a toiletries bag. Not everyone can say they think about Wire every time they shave.

Wire's story, in fact, is also partly that of its fans. Pink Flag remains Wire's masterpiece and manifesto. Here, the 35 minutes were jammed with 21 songs, some as short as jingles, all pared back to the essentials. Wire were grouped with punk because of their minimalism, but it was a minimalism of deliberate austerity rather than self-conscious crudity. Arts students in Watford, the band members tackled their songs as art projects: the title track is an attempt to rewrite ‘Johnny B Goode' using one chord; ‘106 Beats That' is an effort to write a 100-syllable lyric. At the time, in the way of these things, Pink Flag achieved neither commercial success nor critical acclaim. But if you bought it, you played it incessantly, and today no album from 1977 sounds so starkly, uncompromisingly modern.

Chairs Missing (1978) and 154 (1979) smoothed off some of Wire's rougher edges: the lyrics to ‘Outdoor Miner' were inspired by a wildlife documentary about a burrowing insect, but its gleaming pop surface conveyed it to the lower reaches of the charts. It wasn't to last. When their next release centred on one 15-minute song and featured solo-performance art pieces by each band member, their label sent them packing with the timeless censure: "EMI is not the Arts Council."

Which left the fans, who were often quite oblivious of one another's existence, and the more ardent for it. Wire were taken up, improbably, by the hardcore ‘straight edge' movement, disinclined to artistic flourishes, but similarly minimal in their methods: in Our Band Could Be Your Life (2001), Michael Azerrad describes an early Minor Threat gig at which all seven bands on the bill performed a Wire song. Wire became the choice, too, of indie connoisseurs: in 1987 alone, REM performed ‘Strange' on Document, Big Black issued a thunderous ‘Heartbeat' on Headache, and the Rollins Band (as Henrietta Collins & The Wifebeating Childhaters) amped up ‘Ex-Lion Tamer' on Drive By Shooting. These were, moreover, covers as genuine tributes, quite moving - at least to other Wire aficionados - in their sincerity and fidelity.

Wire's members had by now resumed collaborating in a series of projects that brought them into the general vicinity of industrial music, albeit that songs as arch as ‘Kidney Bingos' and ‘Eardrum Buzz' were funnier and cleverer than anything perpetrated by Coil or Nine Inch Nails. From this regeneration came more fans, and the impetus for the compilation Whore (1996), on which 21 performers covered a favoured Wire cut, including My Bloody Valentine's living, loving take on ‘Map Ref 41ºN 93ºW'.

Curiously, though, Wire seems to have come even more firmly into its own over the last little while, having outlived the era of all-powerful major labels and a slavishly fashion-conscious music press, and into one where distribution is chiefly electronic and fan bases are connected as never before. I've bought the live album The Scottish Play (2004), Read & Burn 03 (2007) and Object 47 from the band's website, www.pinkflag.com, which also directs visitors to an email newsletter, a MySpace page and an online forum. When a band with the loyal following of a Wire seeks attention today, it has a host of ways of keeping it.