Bright children from middle and working class families are still missing out on professional careers because of the continuing dominance of elite independent schools, a new government report has warned.

The cross-party panel on social mobility, chaired by the former cabinet minister Alan Milburn, found that access to professions such as law and medicine was becoming more, not less, exclusive.

More than half of the top professional jobs are occupied by privately educated candidates, despite the fact that they account for only 7 per cent of all pupils. Currently 75 per cent of judges and 45 per cent of senior civil servants are privately educated.

The study called on the government to take radical steps to end the "closed shop mentality" that dominates such professions. It said that the opportunity for the highest level of social mobility since the Second World War may otherwise be lost.

The panel suggests that the government should use young professionals and university students to mentor young people and launch a national campaign to raise aspirations.

Speaking this morning, Milburn said: "We have raised the glass ceiling but I don't think we have broken through it yet."

He added: "It's not that Britain doesn't have talent, to coin a phrase - Britain has lots of talent.

"What we have got to do is open up these opportunities so they are available for everybody."

In an article for the Times, Milburn suggests that the government should explore a Conservative proposal to allow greater competition for education places.

"The Conservatives say that city academies should be extended in both primary and secondary schools," he writes.

"They also say, rightly, that the supply of education places could be opened up to greater competition, particularly in areas of underperformance."

Read our cheat sheet for a summary of the story, the figures, and what the commentators are saying.