Nick Robinson met Beckham while filming outside Downing St David Beckham

The footballer, who spoke to the BBC's Nick Robinson on his way out, said Mr Brown was doing "a very good job".

He said they had discussed Beckham's soccer academy and how it might become involved with schools in the UK.

There has been speculation that Beckham might become a World Cup ambassador for England, but he would only say "we will have to see what the future holds".

Beckham, who plays for Los Angeles Galaxy, has been training with Arsenal during the US Major League Soccer close season, so he can be fit for a possible England call-up under new manager Fabio Capello.

I'm very proud to be here tonight David Beckham The BBC's Nick Robinson on the meeting

He told the BBC Mr Brown was very interested in sport, including football, and also "doing a lot for my academy and also getting involved in schools around the country as well."

Asked what he thought of Mr Brown, after his first meeting with the prime minister, he said: "He's a very good man, he's a man who's looking after our country and he's doing a very good job. I'm very proud to be here tonight."

The prime minister has previously said he wants a government "of all the talents" and has invited people from outside politics to advise him - such as people from the business world.

But Mr Robinson said while there would probably not be a formal role for Beckham on Mr Brown's team, the prime minister would be visiting his academy on Thursday, to see how deprived children could be inspired by sport.

Asked about whether he would be involved in England's 2018 World Cup bid - something that would be a matter for the Football Association rather than Mr Brown - Beckham said he was "very interested" but "we will have to see what the future holds".