Downing Street has rejected claims that racism is rife at every level of British life.

The denouncement came after Sir David Calvert-Smith, the head of the Crown Prosecution Service, said that racist prejudices were prevalent in all areas of British life.

He told BBC Radio 4 it was his "firm belief" that Britain is institutionally racist. "Whether we are talking about asylum, whether we are talking about sport even, there are various stereotypical assumptions that are made," he said.

But Number 10 said it did not recognise the sentiments voiced by the prosecutions chief - although a spokesman conceded that there was "a lot of work" still to be done to "build and foster social cohesion".

Sir David's comments had been prompted by two hard-hitting reports, including one by the Commission for Racial Equality, that concluded the CPS had severe problems with racism ranging from segregating its staff into teams to downgrading cases with a racial element.

An 18-month inquiry by lawyer Sylvia Denman, set up after complaints by staff, found institutional racism "has been and continues to be at work in the Crown Prosecution Service".

The Macpherson report defined institutional racism as "unwitting prejudice, ignorance, thoughtlessness and racist stereotyping" and "the collective failure of an organisation to provide an appropriate professional service to people because of their colour".

Calvert-Smith defended the service for being open about a problem that few other organisations had. The CPS and the police had been cast as the scapegoats for the attitudes of society, he argued.

"It is painful for us and the police to be the only organisations in public life that have actually had the courage to admit we have a problem," he said.

"It has been very convenient for everyone else to say 'Oh yes, the Crown Prosecution Service is a racist organisation, the police are all racist, but nobody else is', which I'm afraid is far from the truth."

His remarks brought surprise from the main organisations that work with the CPS.

The Home Office sought to distance itself from the debate. "Clearly it is wrong to say all people are racist. The government is utterly committed to combating racism wherever we find it," said a spokesman.

The Commission for Racial Equality backed away from supporting the comments but urged other institutions to do more to promote diversity.

"Although the days of overt racism are almost gone, throughout the public and private sector much remains to be done to eradicate racism completely," said a CRE spokesman.

Glen Smyth, chairman of the Metropolitan Police Federation, rejected Calvert-Smith's remarks.

"It's piffling rubbish. He's saying virtually everyone is a racist. If that were true, you wouldn't have mixed marriages and mixed sex relationships. Where is the intellectual rigour in that?"