The Flamin’ Groovies, Scala

“Off we jolly well go.” With that, The Flamin’ Groovies’s Chris Wilson announced the arrival of “Shake Some Action”, the band’s classic evocation of rock ‘n’ roll swagger. In 2013, 40 years after it was first recorded, it's still magnificent, a headlong rush of chiming, descending chords and soaring vocals. “If you don't dig what I say, then I will go away,” sang Wilson. And without a mass audience, The Flamin’ Groovies had gone away. Wilson left in 1981 and the band fizzled out in 1992.

Beginning last night with a ragged version of 1973’s “Let Me Rock” was a statement. This return was about reclaiming – or reworking – a story that ought to have resulted in The Flamin’ Groovies becoming one of the world’s biggest bands. But it didn’t work out. Four decades later, the reconstituted band played to a less-than-capacity crowd at the venue where their contemporaries Iggy & the Stooges tore it up in 1972. The Flamin’ Groovies are as important to the pre-punk landscape as the Stooges, MC5, New York Dolls and the rough end of Britain’s pub rock scene, but they’ve never become as cool as their peers.

The Flamin’ Groovies can’t be robbed of the fact they’re responsible for three of rock’s greatest songs

Songs like “Between the Lines”, "I Can’t Hide”, “Yeah My Baby”, "Yes I Am” and “You Tore Me Down” are minor classics. Hearing them last night was a powerful reminder that when they were good, The Flamin’ Groovies were one of the best: delivering classic, direct songwriting with force. Cover versions – "I’ll Feel a Whole Lot Better”, “I Want You Bad”, “Tallahassee Lassie” – seamlessly fit this reading of a rock ‘n’ roll canon. British material was avoided. Last night was like entering a fantasy jukebox.

But with the smooth comes the rough. Mainman Cyril Jordan, in his wig, looked like a spinster school ma’am. Please, please Cyril, ditch the hairpiece. Guitarist and singer Wilson came over like he’d been studying Oliver Reed and veered between Scottish and Liverpool accents. OK, he’s spent a lot of time over here, but… He lobbed a beer bottle to the side of the stage and said the band had a contretemps in a restaurant near the venue before the show. He mentioned the police. He also missed lines and fluffed guitar parts. Until seventh song “I Can’t Hide”, the sound was muddy with only new drummer Victor Penalosa’s cymbals and the higher register of Jordan’s guitar cutting through. Procul Harum’s Matthew Fisher, guesting on organ, was only audible from “I Can’t Hide” onwards

The Flamin’ Groovies can’t be robbed of the fact they’re responsible for three of rock’s greatest songs: “Teenage Head”, “Slow Death” and “Shake Some Action”. That’s at least two more than most bands. All were played last night, even though Wilson wasn’t in the band when “Teenage Head” was recorded. Despite this, they’ve never become a household name. But it partly explains why the audience at this first Groovies headline show in London since 1978 was mostly older and mostly male. It was never going to be otherwise for the reformation of this most culty of cult bands.

The Flamin’ Groovies were too dismissive of the new wave they could and should have ridden on the back of

In one form or another, before being put to bed in 1992, the San Francisco band had been at it since 1966, executing no-frills rock inspired by the British Invasion and what came in its immediate wake. The last sustained signs of life were around 1986/7. Jordan and his vision of what rock ‘n’ roll ought to be are wedded for life. The current four-piece Groovies features three-fifths of the 1971-1981 line up: Jordan, Alexander (on board from pretty much the beginning) and Wilson.

Despite contracts with hip labels – including prime punk-era Sire Records – and brushes with top-drawer producers Dave Edmunds and Phil Spector, the Groovies never made it. Influential American music writer Greg Shaw put them on the cover of Bomp magazine with the deathless headline “Will 1975 be their year?” Having label-mates The Ramones as their support band at London’s Roundhouse in July 1976 just about killed any momentum. The Flamin’ Groovies weren’t going to be the future, however lauded they were in France. They never caught fire. Too wilful. Too dismissive of the new wave they could and should have ridden on the back of. Still, notable fans include the E Street Band's Steven Van Zandt, who engineered their appearance on the Springsteen bill at the Olympic Park last weekend. This show came on the back of that.

Last night’s transcendent romp through “Shake Some Action” and the blistering “Slow Death” will linger. The third encore’s run through Chuck Berry’s “Roll Over Beethoven” won’t. Elsewhere, album favourites generally enchanted, despite the ragged delivery. But it’s unlikely 2013 will be The Flamin’ Groovies’ year.

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Watch The Flamin' Groovies perform "Slow Death" in 1972