Young people from working class backgrounds or ethnic minorities do not get on because they lack the "aspiration" to make it into top jobs, David Cameron has suggested.
The Prime Minister said that such youths needed more help to make them think "they can get all the way to the top".
He also defended the dominance of his cabinet by a privately educated elite saying that he was choosing "from a talent pool" of MPs and pointing to the appointment of the former working miner Patrick McLoughlin as Transport Secretary.
His comments, made as he travelled to India to cement trade relations ahead of the Commonwealth Heads of Government meeting, were a response to Sir John Major’s speech in which he lambasted the collapse of social mobility in Britain.
The Prime Minister endorsed Sir John’s call for action to counter the "truly shocking" dominance of privately educated affluent individuals in powerful positions.
But he insisted it was insufficient just to "make changes and sit back", as some minorities did not feel they could "get all the way to the top".
"You've got to get out there and find people, win them over, get them to raise aspirations, get them to think they can get all the way to the top," he said.
The Eton-educated Mr Cameron said: "I want to see a Britain where no matter where you come from, what god you worship, the colour of your skin, what community you belong to, you can get to the top in television, you can get to the top in the judiciary, you can get to the top in the armed services, get to the top in politics, get to the top in newspapers.
"We are making some progress in those areas but it is not fast enough and we need to go further and faster so I absolutely agree with the thrust of what John Major said.
"You only have to look at the make-up of Parliament, the judiciary, the Army, the media. It's not as diverse, there's not as much social mobility as there needs to be.”
Mr Cameron said Sir John was a "serious and major political figure and ... perfectly entitled to make serious interventions.
"I welcome these debates and points. He has raised a very important issue."
Speaking in response to Sir John's claims on his LBC radio show on Thursday, Nick Clegg said: "I don't think, nor do most people, that it is Grammar Schools that can have an effect on social mobility.
"We've got to get over this barely concealed snobbery that when you leave school you need to go to university. There are many other things. Apprenticeships are an old fashioned idea that I think holds the future solution.
"All the evidence shows that if you give young people the opportunities to take up apprenticeships and don't treat them like second to universities has a transformative effect.
"I support excellence in schools, you can have academic excellence without splitting up children at early stage. It deprives children from fulfilling their potential."