Few things in life have given me greater pleasure than the knowledge that Clive Dunn – the British comedy actor who played Corporal Jones in television sitcom Dad’s Army – chose Arnold Schoenberg’s Piano Concerto when he was invited to appear as a Desert Island Discs castaway in 1971. I love Schoenberg; I adore Dad’s Army. And my joy could only be enhanced if it were to be revealed that Arnold himself reciprocated and, when he wasn’t revolutionising the harmonic basis of Western music, he kept a keen eye on the bourgeoning careers of Dunn and fellow cast members Arthur Lowe, John Le Mesurier and Ian Lavender.

As Jo Malone, the British businesswoman who appeared on this morning’s edition of the programme, has found out, opening up your personal record collection to public scrutiny is an intimate act of personal revelation; right up there with posting your diary or bank statements online. As the programme was broadcast, the Twitter naysayers started pouring scorn. As Elton John’s duet with Pavarotti minced into a track by Coldplay, the horrible aural spectacle ending with Whitney Houston and Queen, Malone was hauled over the social media coals for her anodyne taste in music. Neil Fisher of The Times tweeted ‘This song stinks. ‪#desertislanddiscs ‪#jomalone‘ – the joke being that Malone made her personal fortune out of perfume – while pop-writer Simon Price tweeted ‘Fittingly enough, Jo Malone’s Desert Island Discs is making everyone go…’ – captioned by that familiar photograph of Macaulay Culkin in cutesy 1980s comedy film Home Alone, his hands clasped over his face in mock gothic horror.

To be fair, I’d never heard of Jo Malone until 9.00 this morning, but clearly reputations are there to be won and lost on Desert Island Discs. You’d be surprised to hear Bruce Forsyth or Jimmy Tarbuck choose Pierrot lunaire or The Art of Fugue – they both signed off with a track by Frank Sinatra – but, that said, if Clive Dunn, who let us not forget had a hit record in the 1970s with ‘Grandad’, a maudlin pop ditty about how deeply we all love our grandpas, could chose Schoenberg’s chewy Piano Concerto, anything ought to be possible. No reason at all why Keith Chegwin might not use the opportunity to reveal his love for the string quartets of Roman Haubenstock-Ramati; or Laurence Llewelyn Bowen that he can only tolerate Bach on the harpsichord, otherwise the tuning and phrasing is all wrong, darling.

You wonder why Anthony Caro – the brutalist sculptor, known for his metal constructions – chose nothing at all from the twentieth century; no Stockhausen or Xenakis, who you might think would be his people, but instead a piece of Gilbert and Sullivan. How disappointing to hear the apparently ballsy feminist journalist Julie Burchill opt for Andy ‘Music To Watch Girls Go By’ Williams. And then the most desperate category of all: politicians who exploit the programme to get down with the kids; David Cameron and Nick Clegg uniting in their love of Radiohead, and Tony Blair, before he became PM, standing shoulder-to-shoulder with Bruce Springsteen’s anthemic ‘Fourth of July.’

The poet Ian McMillan chose John Cage’s 4’33’ and comedian Vic Reeves plumped for a song by Marxist avant-rock group Henry Cow. But the sad truth is that Desert Island Discs can too often reveal how lacking otherwise great minds can be when it comes to musical ambition. Which makes Clive Dunn’s decision to unleash the Schoenberg Piano Concerto on to a Saturday morning Radio 4 audience feel ever more admirable.

They probably didn’t like it up ‘em.