The UK could lose its place at the top of world university rankings within 10 years, the vice-chancellor of Cambridge University has warned.
Prof Richard said the UK must retain its competitive edge
Professor Alison Richard told MPs the quality of research in the UK must not be undermined by the drive to raise student numbers.
Ministers want 50% of 18-30 year olds to attend university by 2010.
Prof Richard also said the government must invest more in higher education if the UK was to remain a world leader.
League table rankings published in the Times Higher Education Supplement last year showed that Cambridge and Oxford were among the few world universities to challenge the global dominance of US institutions.
Harvard in the US was top, followed by Cambridge and then Oxford. Britain had 29 universities in the list of the world's top 200.
Prof Richard, who was previously Provost of Yale University in the United States, told the cross-party Commons Education Select Committee: "We have got maybe a decade to consolidate and position the system to retain its competitive edge.
"Having come from 30 years in a very big country, how does this very small island keep its significance in the world?
"We have to operate at the very high end of quality.
"The risk, I see, to the UK system is that with the under-funding of our educational activities historically, the temptation will be to go for volume rather than quality."
Prof Richard also cautioned against the trend for British universities to see foreign students as "cash cows", saying this was dangerous.
International students pay higher tuition fees than British and EU undergraduates, whose fees are capped at £3,000 per year.
But Prof Richard gave a warning that overseas students were not necessarily the best students.
The trend to recruit more foreign students to plug funding gaps could create "a downward spiral" and undermine the quality of universities in the UK, she said.
"That's not happening but that would be the worry if there is not sufficient investment."