David Cameron takes a risk in David Letterman appearance

A New York institution: The entrance of The Late Show with David Letterman Photo: Joel Ryan/PA

After the Prime Minister has finished giving a speech before the United Nations General Assembly tomorrow, there will be some more talking to do - that's if the master of talking on US TV allows him.

David Cameron's decision to go on The Late Show with David Letterman has been described as high risk.

Letterman is no stranger to politicians appearing on his show and when they step onto his territory he is the one who decides the agenda.

Witness London mayor Boris Johnson, who agreed to appear on the show to talk about London's cycle hire scheme. What Letterman asked him was altogether closer to the bone: "How long have you been cutting your own hair?"

It is not the sort of question he'd expect to be asked here.

London mayor Boris Johnson appearing on The Late Show with David Letterman

Then the Former Prime Minister Tony Blair went on the show with a book to plug, but Letterman repeatedly asked whether he concurred with rumours that George W Bush is "dumb". Cue nervous laughter.

I asked Tony Blair's former spin doctor Alastair Campbell whether he thought Cameron's upper-class background would provide ample subject matter for Letterman. After all, Downton Abbey fever is burning in the US so it would be a popular subject matter with his audience.

Tony Blair did not expect to be asked about his view of Former President George Bush's intelligence Credit: Stefan Rousseau/PA Wire.

You can see why the talk show appearance has made some nervous.

With an important UN speech to deliver first, and the Prime Minister keen to promote British business on his visit, there is a danger that appearing on Letterman's show will overshadow all these good intentions.

It could be just the talk show that becomes the talking point.