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Ministers have outlined plans to increase competition between universities.

Institutions will be able to bid for as many top students - those with AAB or better at A-level - as they can attract. It will become easier for private institutions to enter the market, with 20,000 student places reserved for institutions that can offer courses costing below £7,500 per year.

Two university leaders discuss the likely effects of the plans on their institutions.

Professor Peter John, Vice Chancellor of the University of West London, says he supports the idea of using price as a mechanism for driving student choice, and backs competition "as long as it's fair".

But he believes the University of West London, which is charging £7,500 tuition fees, could find itself in the "squeezed middle" under the changes.

This would mean being caught between the universities allowed to expand place numbers for talented students, and those allowed to expand because they are charging the lowest fees.

Institutions such as his may find their numbers are capped below current levels and have to turn qualified students away, he says, especially if overall student numbers decline if students are put off by higher fees.

"Perhaps we may lose 20-30% of our student cohort," he says.

"That's a real concern because we offer students who are the first in their families to go into higher education the opportunity, and to deny that to a large section of the population would be a retrograde step."

Some 58% of the university's intake comes from households with average or below average earnings, and only 14 students are from independent schools, he points out.

He is critical of the plan to allow universities to expand place numbers for students achieving the equivalent of AAB A-level grades or higher.

"I don't think that's widening participation - it is simply sharing out a small number of students into the higher universities. All students that have the required qualifications should be given the choice to go to university and it shouldn't be narrowed to a small number," he says.

David Allen, registrar and deputy chief executive of Exeter University, broadly welcomed the government's proposals for increased competition between universities, including private institutions.

"As far as I'm concerned - bring it on, as long as we're all on a level playing field - I think competition drives down price and drives innovation," he said.

"From our point of view, as one of the top universities, near the top of the food chain, if we can recruit very good students and still provide them with an excellent experience, that's what we would want to do."

But universities more likely to struggle to attract students need to "realise that they're competing in a very competitive world" he said.

Exeter University has some 20,000 applicants for about 3,500 places every year, he says.

But even so, the university is "investing quite heavily" in marketing and will be "very aggressively presenting ourselves" to prospective students at open days, he adds.

The university is spending £400m developing its campuses, and is planning a "contract" between students and the university, outlining what students will get for their money and what is expected of them.

Mr Allen stresses the full "Exeter student experience", which mixes academic study with employment preparation and cultural and sports opportunities, and acknowledges that too much growth in numbers could undermine it.

"We certainly wouldn't want to expand too much… we've invested very heavily so we do have the facilities available … and given that we're not planning a very big expansion I think our facilities will be fine," he says.

He says the current period is the most exciting time he can remember in 36 years working in higher education.

"It's liberating," he says. "If the new regime does free up the market, and reduce or eliminate student quotas, I think it will be very important for the country, and very important for the leading universities to have that choice and diversity and to be masters of their own destiny, rather than told what to do by the government."