The man charged with promoting fair access to Britain's universities has warned of a middle-class bias in higher education, claiming that colleges are "missing a lot of excellence".

Professor Les Ebdon, head of the Office for Fair Access (Offa), said that universities seeking to maximise their income were encouraged to admit "good middle-class" applicants rather than take a risk on disadvantaged students who were more likely to drop out.

As hundreds of thousands of students prepared to receive their A-level results on Thursday, Ebdon claimed that it was vital to retain funding – now under threat – which compensates institutions for accepting youngsters from the least well-off backgrounds.

The £327m student opportunity allocation was cut by 10% by the chancellor George Osborne this year. The fund is at the centre of a row between the highly selective Russell Group universities and more modern colleges and former polytechnics, which benefit from it the most, over whether it should bear the brunt of a further £45m cut to higher education funds announced by Osborne for 2015.

Ebdon, who was vice-chancellor of the University of Bedfordshire until his appointment to Offa in 2012, told the Observer that the fund, similar to the pupil premium cash to support schools with children on free school meals, was a vital counterweight to the middle-class bias encouraged by the current funding system.

"It recognises there may well be additional costs for taking on students from disadvantaged backgrounds," he said. "Those costs are in outreach, or there may be gaps in pastoral education that it is important to fill. But most importantly, non-traditional students are more likely to discontinue their education.

"They may well come from financially challenged backgrounds, and financial challenge is one of the reasons why students drop out of their courses.

"To put it bluntly, if you really want to maximise the income of your university, then you take kids from a good middle-class background whose parents can ensure they don't fall into financial difficulty. I think the student opportunities allocation is extremely important because, while it may only cover half to a third of the additional costs of such students, it is some kind of compensation to those universities."

Official figures released last week show that two-thirds of A-level students from the independent sector went on to Britain's leading institutions in 2010-11 compared with less than a quarter of those from the state sector.

It also emerged that teenagers from the poorest families – those who are eligible for free school meals – were half as likely to progress to a higher education course as their more affluent peers.

Ebdon said it was clear that Britain was "missing a lot of excellence". However, he said that universities, encouraged by Offa, had done more outreach work than ever before in recent years to encourage disadvantaged children and there were now signs for optimism.

In 2004, 18-year-olds in affluent areas were six times more likely to apply to the most selective institutions than those from disadvantaged areas. This year, Ebdon said, the ratio had reduced so that those from affluent areas were just 4.3 times more likely to apply to the most selective institutions, including Oxford and Cambridge.

He said: "So I think we are being able to see some impact now for all the work that universities are doing to widen access. We have been pushing them very hard to engage in outreach activity.

"This is further evidence that our original attempts through bursaries and financial inducements to students have not worked as well as outreach programmes."

Ebdon revealed that Offa's latest strategy paper, to be submitted to ministers shortly, will be to target the parents of disadvantaged children to encourage them to believe that a university education is relevant to their offspring.

"Very often you can get a kid really turned on to it and they go home and the family say: 'No, university isn't for the likes of us, you won't be going'," he said. "You have to engage with a whole family, indeed a whole community, [to encourage them] into believing university is a realistic option for everyone."

A Russell Group spokesman said: "Funding decisions are for the government. As we said at the time of the spending review, when the Higher Education Funding Council for England allocates their budget to universities in 2015-16 it is vital they increase funding for teaching science and engineering subjects, which play a crucial role in underpinning future growth."

But Professor Andrew Wathey, vice-chancellor of Northumbria University, said the student opportunity allocation was the "key to seeking excellent students across the broadest possible social spectrum".