Nobody disputes the fact that the two-man comedy act Flight of the Conchords - “formerly New Zealand’s fourth most popular guitar-based, digi-bongo, a-cappella-rap-funk-folk duo” - are extremely funny. Equally, when they put out an eponymous album earlier this month, containing 15 spoof songs taken from their popular American cable-television series, there were no expectations that it would sell. Most of the reviews were kind in praising the hilarious accuracy of the Conchords’ pastiches of everybody from Pet Shop Boys to Prince. But nearly all were hedged by a conviction baldly expressed in one damning payoff: “Who’d buy a comedy album?”

The answer, a fortnight later, has caused quite a stir. In its first week of release, Flight of the Conchords entered the Billboard Top 200 album chart at No 3. In the UK, where the television show has been confined to the digital channel BBC4, it clipped the Top 40. The only other satirical pop record to have sold in comparable quantities in this century was by Tenacious D, Jack Black’s comic rock turn, whose second album, The Pick of Destiny, made some headway in 2006. It, too, was greeted with scepticism by critics. As one put it: “The only long-term replay value you’ll get from this record will come from playing it for friends who haven’t heard it.”

The prevailing notion here is that pop and comedy are okay for a one-night stand, but can’t sustain a relationship. Comedy records are the point at which pop becomes disposable, and not in a good way. This view is now so entrenched, it’s easy to forget how alien it would have seemed to earlier generations of record buyers.

For about 100 years after Thomas Edison invented the phonograph, humour was the stock in trade of many recording artists. From the Vir-ginian vaudevillian Cal Stewart, who put out rib-tickling stories on Edison’s own label in 1898, to George Formby, the goofy Lan-castrian ukulele-strummer whose cheeky nod to everyday voyeur-ism, When I’m Cleaning Windows, was a radio favourite for years after he died in 1961, pop often aimed to raise a smile.

The advent of rock’n’roll - on the face of it, no laughing matter - didn’t significantly change things. It was having recorded the Goons that first made George Martin cool in the eyes of his wacky young charges the Beatles. Prominent among the slew of beat groups that followed where they led were Freddie and the Dreamers, a troupe whose barmy costumes and choreographed on-stage capers owed far more to British seaside entertainment than they ever did to rock’n’roll. A surprise hit in America, Freddie and co were saluted in 1980 by the celebrated rock critic Lester Bangs for their “plenitude of talentless idiocy” - for which, Bangs argued, they should be not only respected, but “given their place in rock history”.

The British pop charts of the 1960s were seldom without their comedy moments. Nor were these regarded as fodder for old “squares”. Though he chooses to play it down these days, David Bowie made his chart debut with The Laughing Gnome, a song heavily influenced by the actor, song-writer and wit Anthony Newley. Newley, who worked on a record called Fool Britannia, with Peter Sellers, and released a Christmas single, Santa Claus Is Elvis, was only one of the popular 1960s acts who regarded satire and pop - both recently reinvented and deeply fashionable - as natural partners.

Several bands emerged whose chief raison d’être was to take the mickey out of other pop groups. The Barron Knights started the trend in 1964 with Call up the Groups, a medley themed around an imaginary return to National Service, in which they parodied the Beatles, the Rolling Stones and the Dave Clark Five, whose monster hit Bits and Pieces they reworked as Boots and Blisters.

As the decade wore on, and pop started to take itself more seriously, along came the funniest band of the lot, the Bonzo Dog Doo-Dah Band. A surreally attired ensemble led by Viv Stanshall, a foppish fellow with big glasses, they mercilessly teased rock’s earnestness with songs such as Can a Blue Man Sing the Whites? - and so hip were they in their day, Paul McCartney, no less, co-produced their hit single I’m the Urban Spaceman. Their enduring appeal is reflected in the name of the American indie band Death Cab for Cutie, taken from the title of a song the Bonzos performed in the Beatles film Magical Mystery Tour.

It was after the Bonzos broke up, in 1970, that comedy and rock began to drift apart. In the glam era, parody became redundant as Roxy Music, David Bowie and others incorporated irony into their act. How could you make fun of an artist such as Bryan Ferry, whose quiff and glitter suits were themselves a kind of retro joke? Punk definitely had its funny side – it was partly conceived as a loud raspberry in the face of Pink Floyd and other humourless “dinosaur” rock acts. The punks were intent on having an old-fashioned laugh, and they particularly loved the cockney music-hall patter of the late Ian Dury.

Yet, once a new crowd of self-styled “alternative” comics arrived at the end of the 1970s, and comedy gigs competed to attract the same crowd that went to rock shows, everything changed. From then on, pop music and comedy were seen as separate ventures. This is presumably why it never occurred to Ricky Gervais to employ his comic skills during his youthful spell fronting an unsuccessful pop band, and why the audience that loved Steve Coogan’s jokes conspicuously failed to turn up for his incarnation as a faux-crooner. His 1997 album I Am Tony Ferrino stiffed badly.

For the past 30 years, pop music and satirical humour have tended to get together only on special occasions. The two that everybody remembers are the Rutles, the former Python Eric Idle’s spoof of the Beatles, and Spinal Tap, the American actor and director Christopher Guest’s larky send-up of an idiotic English hard-rock band. Successful as these were as filmic events, music wasn’t really their point. The antics of the characters dwarfed a set of intentionally average songs whose amusing lyrics were not enough to make them memorable.

It’s good to report, then, that Flight of the Conchords may, just may, be bucking an established trend. Not only does their album do a brilliant job, lyrically, of skewering pop’s many absurdities – from its overblown sexual swagger to its obsession with alienation, robots and anything suggestive of teenage dysfunctionality – their songs are melodically effective and cleverly arranged. In short, the spirit of the Bonzos is back. The question isn’t “Who’d buy a comedy album?”, but “Who wouldn’t buy this one?”

The Bonzo Dog Doo-Dah Band play the Astoria, WC2, on June 6

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