In an awkward appearance on Letterman’s “Late Show” on Wednesday, filmed in New York, Cameron failed to guess the composer of the hymn “Rule Britannia” or the meaning of “Magna Carta”, an early English charter of rights.

“You have found me out. That is bad, I have ended my career on your show tonight,” Cameron joked on the influential CBS show, which is watched by around three million Americans every night.

Britain’s Independent newspaper said Cameron had suffered a “humour and history failure”, while some commentators jokingly suggested the prime minister should be deported for failing the mock “citizenship” test.

Cameron, 45, who was educated at the elite Eton boarding school and Oxford University, wrongly guessed that Edward Elgar composed “Rule Britannia” — the poem by James Thomson was in fact put to music by Thomas Arne.

He was also baffled when Letterman asked what “Magna Carta” means. It translates from Latin into English as “Great Charter”.

As the first serving British premier to appear on the long-running show, Cameron was welcomed on to strains of “Rule Britannia” before Letterman inquired if he minded being asked some “dumb American questions”.

The prime minister fared better during other parts of the grilling, correctly identifying the date of Magna Carta’s signing as 1215 and explaining the difference between Northern Ireland and the Republic of Ireland.

He also won applause from the audience when he hailed the success of the London Olympics.

The British press had warned Cameron of the perils of appearing on the “Late Show”, as 65-year-old Letterman is known for his irreverent questioning.

When London’s dishevelled mayor Boris Johnson was a guest on the show in June, Letterman asked him if he cut his own hair.

Some commentators on Thursday suggested that Cameron, who was in New York to attend the UN General Assembly, appeared on the show in a bid to outshine Johnson, seen in Britain as a potential future Conservative leader.