The prime minister, who believes he has a sharper wit than his fellow Etonian, appears to think he will have little difficulty in coping with the CBS host.
No 10's approach suggests that Cameron may not have brushed up on Letterman's razor-sharp approach. Johnson was almost stumped for words in June when Letterman asked him how long he had been cutting his hair.
Downing Street said of the prime minister's appearance, which will follow his speech to the UN general assembly: "Around a busy schedule of bilaterals and diplomatic work, the prime minister will seize on the legacy of the London Olympics to further promote Britain as a guest on CBS's Late Show with David Letterman. Reaching on average over three million viewers a night, the prime minister is due to appear on Wednesday's show to highlight all that Britain has to offer and to encourage more Americans to visit or to set up a business here."
Letterman may swot up on British business and ask the prime minister earnest questions about opportunities for US businesses in Britain. Then again he might ask the prime minister about life as a fifth cousin of the Queen.
Andrew Mitchell, the chief whip, is hardly a household name in the US. But Letterman may be tempted to ask the prime minister about Britain's public schools as Mitchell, known as "Thrasher" at Rugby School, fights to save his political career.
Cameron may follow the example of Barack Obama who sailed through his recent appearance on the Letterman show. But then Obama handed Letterman a scoop – his first television interview since Mitt Romney dismissed 47% of US voters as benefit scroungers.
In one of his first engagements in New York, Cameron will issue a stern warning to world leaders to do more to meet the eight millennium development goals before a deadline in 2015. It is widely believed that the developed world, which had pledged to eradicate extreme poverty and hunger and achieve universal primary education, is way off track.
The prime minister, who will co-chair the first meeting of the UN high level panel on the post-millennium development goals, will say: "Less than half of the 142 objectives that underpin the eight MDGs are on track to meet the 2015 targets. So the first thing we must do is send a clear message to everyone who signed up to millennium development goals – that now is the time to step up and honour those promises.
"I know there are some who say we can't afford to do that right now. They believe we have to focus on ourselves. And if that means breaking promises, then they're sorry – but it just has to be done. Well I'm sorry, but it doesn't.
"When we make a promise to the poorest people in the world, we should keep it – not turn our back on people who are trusting us to help them. More than five thousand infants die every day from preventable diseases like pneumonia and diarrhoea. So to those who say we can't afford to act. I say, we can't afford to wait."
The prime minister will reaffirm his commitment to meeting the UN target of spending 0.7% of gross national income on overseas aid by 2013. He will also outline Britain's role in helping to vaccinate more than 12 million children against preventable diseases and supporting 5.3 million children to go to primary school.
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