The deputy prime minister, Nick Clegg, will warn vice-chancellors universities have become "instruments of social segregation" as the government prepares to set new targets on widening access to institutions charging more than £6,000 a year.

Universities that want to charge fees of up to £9,000 a year will be pushed to widen access to pupils from state schools, in guidance to be published on Thursday.

Ministers are concerned by the disparity between the number of privately educated pupils in England and the intake of Oxbridge and the other most selective universities.

Clegg's aides drew attention on Monday to the fact that just over 7% of children in England go to private schools, but go on to make up 75% of judges and 70% of finance directors.

While the number of teenagers from poorer backgrounds attending university has gone up in recent years, they have tended to go to less selective universities.

A source close to Clegg said: "These statistics demonstrate just how closed many of our universities are to students from disadvantaged backgrounds. Universities should be the greatest agent of social mobility that we have in this country, but too often instead they are serving as instruments of social segregation."

Simon Hughes, the government's adviser on access to higher education, has said universities should drastically limit their intake of privately educated pupils, to reflect the proportion in society. Ministers will issue guidance to the government watchdog, the Office for Fair Access (Offa), which will draw up access agreements with individual universities.

Draft guidance published last year said that universities' "level of ambition" for widening access should be proportionate to how much they seek to charge.

The agreements will be reviewed annually. Universities that fail to make progress could be stripped of their right to charge higher fees or fined a maximum of £500,000.

The government is also due to outline more details of its national scholarship programme for bright children from poorer backgrounds, which is intended to support 48,000 students a year by 2014.

The deputy prime minister will host a meeting with vice-chancellors on Thursday to discuss their response.

The source added: "Nick knows that our reforms to higher education will have failed if we do not achieve our stated primary goal of getting more kids from poor backgrounds into university and particularly into our top universities.

"We're not going to be able to throw open the doors of our elite institutions without working with the universities themselves to improve access.

"Nick will be making clear to vice chancellors what he expects of them when they meet this week."

Labour questioned whether Offa had sufficient staff to monitor universities. Gareth Thomas, the shadow higher education spokesman, said: "Bearing in mind Offa has just three staff to help its director enforce access agreements across 130 universities, the idea that universities will face rigorous checks before they can charge £9,000 in tuition fees is difficult to believe."

Thomas also criticised the government's decision to cut the number of university places by 10,000 next year. Ministers say the demographics show there will be less people approaching university age by then.

Newer universities are concerned that the government may restrict institutions with high drop-out rates from charging higher fees.

Pam Tatlow, chief executive of the university think-tank million+, said: "Many students make perfectly sensible lifestyle decisions not to continue with their course for family or financial reasons.

"However, many return to higher education at a later date and they all have to pay any loans that they have taken out. Universities are working very hard to support students to succeed but the government must be even-handed in its approach to access and retention in any guidance which it issues to Offa."