Universities should drastically limit their intake of privately educated pupils if they want to charge undergraduates up to £9,000 a year, says the government's adviser on access to higher education.

Simon Hughes, also the Liberal Democrat deputy leader, warns that universities need to be far more active in seeking out the brightest state school pupils.

He said: "I think my message to the universities is: You have gained quite a lot in the settlement. Yes, you've lost lots of state money, but you've got another revenue stream that's going to protect you. You now have to deliver in turn. You cannot expect to go on as you are. It has failed miserably."

Just over 7.2% of pupils in England attend private schools but make up over a quarter of the intake at the 25 most selective universities, and 46.6% at Oxford.

Before his first meeting next week with Vince Cable and David Willetts, the coalition ministers who oversee universities, Hughes told the Guardian: "Every university should, wherever their fee level is, but specifically for a fee level above £6,000, recruit on the basis of no more people coming from the private sector than there are in the public as a whole ... I don't believe you have to look to the private sector to give you the quality of exam results and ability to make up the numbers to fill the places."

One of Hughes' key tasks in his new role is to frame expectations of universities which seek to charge fees above £6,000. His comments echo the view of the deputy prime minister Nick Clegg, who has said there were disproportionate numbers of middle and upper class students at university.

But the criticism of private school dominance will make the coalition's Conservative partners uneasy.

Ministers have issued draft guidance on access which says universities will be expected to set targets for applications and entrants from disadvantaged backgrounds but will be judged on the "prevailing trend … to avoid placing undue focus on a single data point". The guidance has been criticised as vague by the National Union of Students.

Hughes said: "If you're really going to be radical about these things, then you have to say 'access' means you seek to reflect society in your recruitment policy. And most people in society go to local authority schools, not to private schools, and therefore most people from all universities, including Russell Group universities, should do that. And it doesn't mean lowering standards."

Dr Wendy Piatt, director general of the Russell Group, said its universities were committed to attracting students with the most talent from all backgrounds. "Admission is and should be based on merit. We seek out students with the enthusiasm and ability to flourish." she said.

"There has been a real increase in numbers of students at our universities from lower socio-economic groups, but we remain concerned that too few students from comprehensive schools are among the highest achieving candidates. The primary reason ... is underachievement at schools."

Hughes said universities should be expected to address the gap from 2012, when they can charge higher fees.

"If new students are starting at universities in the autumn, 2012, then the new regime has to start from then, and that means the selection process – there's no reason why the [higher education] white paper and the bill this year, which will be on the statute book, I assume, by the beginning of the next academic year ... shouldn't have a clear admissions criteria that will allow the recruitment policy to work better."

Privately educated children have a far better chance of getting into the most selective universities because their performance at GCSE and A-level outstrips that of pupils in the state sector.

In last summer's A-level results they were three times more likely to get the top A* grade than comprehensive pupils.

However, research carried out for the government has shown that pupils from comprehensives are likely to do better at university than private or grammar school pupils with similar A-level results.

Giving the example of a "fantastically bright" woman from his own south London constituency, Hughes said: "People like her ... just never get the opportunity, because there is no real pressure on universities to go out looking in schools like the one she was at. And we've just got to change that. So for me – of all the bits of the jigsaw, that for me is where I want to have most influence, and I want to try and persuade them that they have to be really tough with the universities, really really really tough."

Hughes praised some university access schemes, including King's College London's access to medicine course, but said: "Even if some of the schemes have been fantastic they are not being rolled out across the country."

Hughes, who was educated at private schools in Wales and Selwyn College, Cambridge, also said that universities charging above £6,000 "must be the exception" and not the norm.

His unpaid role will involve challenging "misinformation" which might deter young people from poorer backgrounds from applying to university.

In the interview, Hughes said he wanted to focus the debate on the lower figure of £6,000 a year.

"I mean, unless government fails, the exception will be more than six. So we should be talking about six. We should be talking about 18 grand for three years, not 27 grand or more. It's the amount – three lots of £9,000 plus anything else. £6000 is not great, but it's a much more manageable increase."

The terms of reference of his role stress that his main task will be "the effective communication and delivery" of the government's policy, within the current budget.

But he is also expected to transmit the views of young people to ministers and make recommendations on policy.

Hughes plans to examine the system of maintenance grants to leave students with lower debts for their living costs.

He said: "I don't have the authority to suddenly increase the amount of money in the pot, but there may be deals we can negotiate, there's the student loans company to talk to, talk to the private sector, there's the business community."

He is keen to ensure that students from less privileged backgrounds are not deterred from doing longer courses including medicine.

He said: "We need to probably renegotiate the deal with the NHS, which has been part of the background on that." Part of the funding for medicine and dentistry degrees is a settlement from the department of health and the NHS.

One of the first items on his agenda will be the successor to the educational maintenance allowance, a grant of up to £30 a week aimed at encouraging poorer children to stay on education after 16. Hughes is critical of the decision to scrap the scheme, which is due to close to new applicants in January. Ministers claim 90% of students receiving the EMA would have stayed on anyway and say that a more targeted replacement is required.

Hughes said: "I have committed myself to saying something about EMA by the end of the month. To replace a system that is fixed and certain by a system that is discretionary seems to me to be problematical ... people need to know that certain things will be funded or certain payments will be met."

Tim Hands, master of Magdalen College school, Oxford, and co-chair of the universities' committee of two independent school groups – the Headmasters' and Headmistresses' Conference and the Girls' Schools Association – said: "Universities should be free to select the best candidates, regardless of background. The best should not be discriminated against on political grounds. At a time when the economy is under threat, to tamper with our intellectual economy is misguided."