Cameron became the first sitting prime minister to appear on the show, and was surprised by his host when Letterman put him through a mock British citizenship test, quizzing him on British colonial history and his cultural knowledge.
“You have found me out. That is bad, I have ended my career on your show tonight the PM said as he struggled to find the answers to his host’s questions.
When asked about Magna Carta, Cameron speedily shot back with 1215, the year in which it was signed, but was stumped when Letterman asked him what the English translation meant (Great Charter, fact fans!).
Cameron also came unstuck when he was asked about the composer of Rule Britannia, to which he responded “Elgar”, only for Letterman to reveal later that the correct answer was Thomas Arne.
The show had an English theme, with actor Jonnie Lee Miller, who was born in Kingston, Surrey, and nu-folk band Mumford and Sons, from Wimbledon, the other guests.
Cameron follows in the footsteps of Boris Johnson and US President Barrack Obama, who have both appeared on the show before.