Kate Moss wanted David Cameron's number because she thought he was a plumber

The pair were introduced by Top Shop supremo Sir Philip Green at a charity dinner.

A starstruck Mr Cameron had no idea what to talk about - so ended up having a conversation about flood damage.

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The supermodel ended up asking him for his phone number so he could give her advice on drainage.

Appearing on ITV1 show Parkinson, Mr Cameron was asked about the "fun" side of his job.

"I suppose you get to meet some quite interesting people," he said.

"I went to a charitable dinner the other night and Philip Green came up to me and said, 'Would you like to meet Kate Moss?' So I said, 'Well, of course I'd like to meet Kate Moss.'

"I went over to her table and on the way over I thought, what on earth am I going to say?

"And I remembered she actually has a house in my constituency and we'd had these terrible floods in West Oxfordshire and so I said, 'Very nice to meet you, very sorry about the flooding in your house.

"I know your local pub has been flooded, I've been to see the publican and I know you like to go to the pub and so I know it's going to re-open in six months.'

"So I went on like this, twittering on, and she turned around and said, 'God, you sound like a really useful guy, can I have your phone number?"'

Mr Cameron went on: "I went back to my table and said, 'The good news is, I met Kate Moss and she wanted my telephone number. The bad news is, I think she thinks I'm something to do with drainage."'

The Tory leader was a guest on Michael Parkinson's show alongside Formula One star Lewis Hamilton, singer James Blunt and actor Sir Ian McKellen.

Parkinson compared the rivalry between Hamilton and fellow driver Fernando Alonso to the relationship between Mr Cameron and Prime Minister Gordon Brown.

"You don't like him much, do you? He's your Alonso, really, isn't he?" the presenter asked.

Mr Cameron replied: "It hasn't got that bad yet. The truth is that I really don't know him very well. We see each other at official events and we talk a little bit but I don't know him very well.

"The truth is, we just don't agree about big things, about the future of our country and how we should run things... we should work together, of course, but where you disagree I don't think you should hide it."

Mr Cameron admitted that his CV was "pretty corny - went to Eton, went to the Treasury. I accept it's not a hard luck story. I went to an amazing school and I had a very privileged upbringing."

He also spoke about the challenges he and wife Samantha face in bringing up their disabled son, Ivan.

"I don't think it has changed me completely as a politician but it has certainly made me think a lot about politics, the health service and things we need to do to help families," he said.

"We are lucky, though. We are wealthy and we can afford to get extra help. But all of us who are parents of disabled children are not angels - some people are angels and do a fantastic job, but most of us are just normal mums and dads trying to do our best. But it's a huge struggle and you need a lot of help."

•Parkinson is on ITV1 tonight at 10.35pm.