Former minister Alan Milburn has chaired a study for the prime minister on widening access to high-status jobs.
He says young people in England should have access to much better careers advice to boost their ambitions.
Mr Milburn told the BBC: "We have raised the glass ceiling but I don't think we have broken through it yet."
He said the professions had a "closed shop mentality" and "have become more and not less exclusive over time".
The use of the word 'glass' to denote invisibility demonstrates that there is no actual evidence of such a barrier. If I want to believe in the presence of an all powerful force that no one can actually detect then I'll become a vicar. The phrase 'ceiling' suggests that it is those right at the top of their professions who are trying to keep others out. In fact he implies that professionals are actually trying to keep certain people out, despite the absence of evidence for such a proposition.
I would be surprised if any occupational group has undergone such a strong demographic transformation as doctors, who 40 years were overwhelmingly white and male, but who are now disproportionately female and Asian. Yet we are supposed to believe that they are preventing the poor from following in their footsteps through some kind of 'closed shop'.
Milburn shouldn't worry about the glass ceiling and instead look at the concrete front door.