David Cameron last night avoided a banana skin of his own making, emerging relatively unscathed from his self-imposed interview with American chat show king David Letterman. Given the host’s history of cutting questions, there had been fears that the British prime minister – who had put himself up for the gig as a breezy diversion from a heavyweight speech at the United Nations – would be embarrassed. While those fears proved unfounded, Cameron didn’t particularly shine either, leaving critics to question the ultimate usefulness of the exercise.

The closest we came to career suicide was Cameron failing to answer a couple of obscure British-history questions – who wrote “Rule Brittania”? (Thomas Arne and James Thomson, not Elgar), and what does “Magna Carta” mean? (Great Charter) – but the PM was easily able to explain the significance of the latter and the date it was signed, as well as providing a lowdown on the political situation in Ireland and Wales, and the UK’s own relationship with America.

However, the alleged reason for appearing in the first place – to advertise and boost British trade and industry in the wake of the Olympics – did not get much screen time, and it was left to viewers to ponder the exact purpose of the visit.

A strong, alternative explanation perhaps lies in Cameron’s desire to deal with the cloud that has lurked above him for the past few months: his Tory colleague Boris Johnson, who appeared on the show in June with considerable aplomb. But Johnson, with all his experience on numerous chat shows and multiple editions of Have I Got News For You – not to mention his rather more natural affability – was always going to outshine the Premier, and so it proved. Meanwhile, Cameron’s cautious respect for the host, and particularly his reputation for tripping people up, meant that he was never really going to go for broke in the first place.

It was, all in all, a rather baffling encounter… but perhaps Cameron simply wanted to do something – anything – to paint himself in a more positive light. As he himself said on air, he is “not very popular at the moment”.