So, David Cameron, is your top track 'Money' or 'Us and Them'?

David Cameron claims that Dark Side of the Moon is his favourite album. Yeah, right says John Rentoul – these days, politicians' pop picks come direct from the focus group

Well, he obviously couldn't say again that The Queen Is Dead is the best ever album, in Her Majesty's Diamond Jubilee year, could he? It is not even the best Smiths album. So he could have said Meat Is Murder, but that would have been to contradict what he had said before, so he did what politicians usually do, which is to answer the question that they want to answer rather than the one that they were asked.

So David Cameron pretended that the Great British Music people had asked him: "What album do most people think is quite good?" At least he was not as transparent as Tony Blair, who once said: "I like the sort of music that everyone likes." The odd thing about Blair is that he has some quite distinct – and awful – musical taste of his own, but when he went on Desert Island Discs his selection went through a scrutiny process more stringent than that for the Brit Awards, with all the yoof in his office consulted on what selections would least open him to ridicule.

Even then, he chose a track by Lenny Kravitz. In the cause of biographical research I had to listen to a whole Kravitz album in a doomed attempt to understand my subject. Blair had a hard enough time, with his suspect association with Simply Red, REM and Foo Fighters. He showed that it is never possible to fool any of the people when it comes to musical authenticity. (Still, he did a better job on the radio show than Cameron, who picked Benny Hill's 1971 hit, "Ernie (The Fastest Milkman In The West)" as one of his choices).

But Blair never suffered in the way that Gordon Brown did. Brown was widely derided for saying that he liked the Arctic Monkeys, which was one of the great myths of his career. The truth is that the interviewer – for New Woman magazine in 2006 – asked him if he liked the Arctic Monkeys. Brown said only that "they would certainly wake you up in the morning".

Far from trying to get down wit da yout, Brown was trying to show only that he knew that they exist, and that they tend to like noisy music. It was his way of saying that he had heard that the Arctic Monkeys were a popular music combination. At least Blair had actually been in a band. And at least I had not chosen to write a biography of John Major. When he surprisingly became Prime Minister in November 1990, the only footage that the BBC had of his private life was from a profile shot by my colleagues on On The Record, the Sunday politics show. This was filmed in about 1989, when he was Chief Secretary to the Treasury, and it featured our man in a comfortable jumper at home putting an Acker Bilk CD in the player.

Acker Bilk, for those who don't know, was like the Dark Side of the Moon for the generation a bit older than David Cameron and me: once cool, now less so. Similarly, younger people would not understand our searing migraine at discovering that Pink Floyd has been classified by iTunes as "soft rock".

Demographic rock: Who's the PM courting?

44% Ex-hippy accountants.

5% Radiohead members.

24% Wizard of Oz nerds.

18% Stoned students.

8% Staff at Mojo magazine.

1% Tory politicians.