Heaven 17, Corn Exchange, Brighton

Heaven 17 never toured during their Eighties heyday, a fact acknowledged wryly as Glenn Gregory declares: "Thirty years late." Time's a funny thing. Last time I saw Heaven 17 was on 2008's Sheffield-centric Steel City package tour, which – though a glorious celebration of the musical legacy of what is essentially England's Detroit – felt somehow reproachful, a reminder of an unrequited future abandoned by the rockist Nineties.

If a year's a long time in pop, two years is an eternity, and the participants of that jaunt suddenly feel newly relevant. Heaven 17's recent collaboration with La Roux received a record 1.2 million hits on the BBC's red button, while the Human League – Steel City tour-mates, friends/rivals and, of course, the band from whom Heaven 17 originally split – are about to release their first new material in a decade: the storming "Night People", which sounds utterly magnificent over the big speakers when Mark "Back to the Phuture" Jones drops it into his warm-up DJ set.

The pretext for Heaven 17's current tour is the 30th anniversary of their classic debut, Penthouse and Pavement (just reissued, somewhat inevitably, in deluxe double-disc format). Never a massive seller at the time – it reached No 14 – P&P has since attained cult status. A prescient satire on social trends (particularly the then-imminent rise of the yuppie), it was politicised yet playful, didactic yet danceable, as epitomised tonight by tracks like "Let's All Make a Bomb", "(We Don't Need) This Fascist Groove Thang" – banned, bafflingly, from Radio 1 by Mike Read – and "At the Height of the Fighting (He-La-Hu)".

It's an album that single-handedly gives the lie to the brainless notion – which has sprung up in more recent times – that the New Romantic era was an amoral, hedonistic celebration of Thatcherite excess. A bitterly ironic commentary from a band who were based, lest we forget, in the industrial North, it's 10 times cleverer than its detractors will ever know. It's also 20 times more fun than that description makes it sound.

Accompanied by visuals from Ian Anderson of legendary Sheffield collective Designers Republic, its crisp electro-funk is sounding ridiculously contemporary, even if the rapid word rate leaves Gregory breathless: the songs, he explains, were tailored for the MTV age, with no thought given to the need to inhale between lines.

Original member Ian Craig Marsh has retreated from the pop life for one of academia (right here in Brighton, coincidentally), so the H17 frontline now consists of fellow founder Martyn Ware, singer Glenn Gregory – or "Gwen Gleggory" as Jools Holland Spooneristically introduced him the other week – and Brighton girl Billie Godfrey, who lends her formidable lungs to Carol Kenyon's bit on "Temptation" and Tina Turner's bit on the, er, Temptations' "Ball of Confusion", one of two selections from Heaven 17's covers-based side project BEF (British Electric Foundation). The other is "Wichita Lineman", the romantic beauty of Jimmy Webb/Glen Campbell's original given a dark undercurrent by the addition of a sinister, anti-melodic root note, the same trick Ware had previously executed with the League's version of "You've Lost That Lovin' Feelin'", and indeed the trick the Orb borrowed when undermining Minnie Riperton's "Loving You" on "A Huge Ever Growing Pulsating Brain That Rules from the Centre of the Ultraworld".

The memory of one guest on the original BEF album, Billy Mackenzie, is honoured with a rendition of the Associates' "Party Fears Two", whose heady, exhilarating rush is decelerated to a more reflective, gentle waltz. Gregory – a friend of Mackenzie who even named his pet whippet Billy – wisely doesn't attempt to match the great man's soaring falsetto. Nobody ever could.

A crowd-pleasing hits section follows, and the housed-up, Nineties-sounding extended version of "Temptation" actually feels more dated than the original (a cautionary tale for any 'heritage' act inclined to jiggle their classics into contemporary shapes). However, existential electro-soul epic "Let Me Go", Heaven 17's favourite song of theirs (and my favourite too), remains untouched, and therefore untouchable.

The ghost of the Human League, whose home-town show I was due to review before it was snowed off, makes several appearances. Ware pointedly sticks his flag in the early League oeuvre with an encore of "Being Boiled" (the Travelogue album version, synth-nerds), that impassioned and ever-bizarre karmic critique of the farming of silkworms, and cue for a bout of mass overhead handclapping.

And, strapping on what must surely be the most sarcastic acoustic guitar on earth, Gregory starts strumming a familiar melody: "Don't You Want Me". During this least likely of covers, Ware heckles, "I could have written this. I'd be rich by now..." He's not bitter, though. In effect, that song, he tells me later, bought his first house. He gave Phil Oakey's faction the rights to the Human League name in exchange for 1 per cent of their next album, which happened to be Dare.

Heaven 17's pavement days were over.

Next Week:

Simon Price visits the endangered 100 Club for The Fuzztones, and finds out whether Frankie can tug at his Heartstrings.