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By Noel Young, Correspondent

September 27, 2012 | 4 min read

British Prime Minister David Cameron strode on to the “Late Show with David Letterman” last night - the first time a sitting British prime minister has appeared on an American chat show - to the stirring strains of Rule Britannia.

Cameron and Letterman Picture:CBS

Then he was flummoxed when Letterman asked: "Do you mind if I ask you some dumb American questions?" "Fire away," said Cameron.

"Who wrote Rule Britannia?" asked the wily Letterman.

"You're testing me there," said the prime Minister. "Elgar?" he suggested. "Edward Elgar?", asked Letterman. " "I reckon," said the PM, not at all sure.

"We can check," said the helpful American host. And check it his underlings did.

After the break , Letterman delivered the news: Rule Britannia was written by James Thomson (a Scotsman) with music by Thomas Arne.

Cameron carried off the embarrassment rather well. In the slightly surreal world of American late night television, with puffs of London fog and awful jokes about Iranian president Mahmoud Ahmadinejad (First name rhymes with manure) he had some important things to say.

Cameron had spoken that day at the UN where the Middle East - the Arab spring and Syria - was his subject. The murder of the American ambassador in Libya was horrific he said but we should stick with the growth of democracy in the region.

He is also sticking with the £, he told Letterman. "It would be bad to join the Euro. You have 17 different countries going in different directions.

"It's very important to keep the (British) currency."

In the end he could see a single government for "a country called Europe . . .I prefer a country called Great Britain," said the Prime Minister.

He and Letterman jousted over the Magna Carta, where it was signed and what it meant. Cameron didn't seem to know too much about that either, although he got the date right: 1215. "I'll send you a copy, " he promised Letterman.

But, despite his Eton education, he was stumped when asked for a literal translation of the Latin name – Great Charter.

‘It would be good if you knew this,’ Letterman said.

‘Yes, it would,’ the Prime Minister replied. ‘You’ve found me out. I’ve ended my career on your show tonight!’

Britain's imperial past had "some good bits and bad bits," said the PM. Britain and America had had their falling out, including burning the White House in the War of 1812, "but things are better now," said Cameron.

The PM said Britain and the US respected each others's traditions : one of which was the Americans' constitutional right to bear arms. Cameron didn't say it - but this is one issue many Brits in the USA regard with disbelief .

Letterman asked about the difference in the two countries' election processes: with each party spending $2-$3 billion in the US. Nothjng like that in Britain, said the PM :We ban political advertising on television . Loud applause from the audience. Obviously they've had enough of the constant attack ads

Cameron talked about the the Irish peace process and Wales, where they speak Welsh.

The Olympics and the Paralympics had been a wonderful double event for Britain. And Cameron made no bones that they were "shamelessly" pushing this success to drive inward investment in Britain.

Despite Britain's economic struggles over the past few years - "the biggest banking collapse" - one bright spot was the creation of a million new jobs, brought about, said the PM, by a "business friendly government".

All in all it was a good performance by the PM. His remarks about a European superstate were much more significant than his Rule Britannia boo-boo . But, hey, you've got to get a headline,

In keeping with the slightly wacky nature of the show, Cameron's 26 minutes in the Letterman limelight ended with a discussion about the No 10 Downing Street cat