Black and Asian school-leavers are more likely to go to university than their white counterparts, it was emphasised today as a leading headmaster claimed none of the three main political parties had serious policies for tackling the lack of social mobility in the UK.

Two out of three state secondary schools do not send a single pupil to Oxford or Cambridge, according to new figures from the Department for Education. The figures also showed around one in seven schools (335) did not send a pupil to any of the 24 Russell Group universities. The grouping represents 24 of the most selective higher education institutions.

Asian students are the most likely to study at a top university, with 12 per cent going on to a Russell Group university – including Oxford and Cambridge – compared with 11 per cent of white students and 6 per cent of black students.

The figures, for 2012-13, also show the percentage of state-school pupils going on to university dropped from 53 per cent to 48 per cent in the first year that fees increased to up to £9,000. By contrast, 60 per cent of privately educated pupils went on to university – 46 per cent of them to those ranked in the top third.

The figures came as Sir Anthony Seldon, master of leading independent school Wellington College, in Berkshire, told an audience in Oxford: “Neither the Conservatives, nor Lib Dems, nor Labour are prepared to take the radical steps that are necessary to ensure that the most disadvantaged in Britain have a top-quality education that would open up the way to top university places and successful careers.” Sir Anthony, delivering the annual “access lecture” at University College, Oxford, said the 80 per cent of pupils who neither attended top state schools nor independent schools “have meagre opportunities for gaining places at top universities and going on to positions of influence”.

“It is a deplorable waste of talent, it is hugely inefficient for the economy and is grossly unjust socially,” he added. He said that “to imagine that current policies are going to produce the radical change that we need to see is naïve at best and delusional at worst”.

Sir Anthony’s comments come a week after a row erupted in the arts world when shadow Culture Minister Chris Bryant cited singer James Blunt and actor Eddie Redmayne, both former Etonians, as evidence of how the arts were becoming dominated by an elite.

Sir Anthony said of schools: “At present, better-off parents either pay for a privileged education… by paying school fees at independent schools or, increasingly, they are paying premium house prices in the catchment areas of top state schools…”

He outlined a five-point plan to tackle social mobility – including reserving 25 per cent of places at outstanding independent and state schools for pupils entitled to the “pupil premium”, extra cash given for every free school meals pupil in state schools.