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Oxford University's vice-chancellor has warned that a lack of funding will make it difficult to compete with international rivals.

Professor Andrew Hamilton warned that the UK's universities would struggle to compete for the best research students in the "global market for talent".

This was not only about competing with top US universities, but also China and India, said Prof Hamilton.

The UK's higher education sector would "increasingly lose out", he said.

In his annual speech, Prof Hamilton highlighted concerns about funding for postgraduate research.

"When other governments are ramping up investment in higher education, particularly for research, treading water will not be enough," he said.

There have been concerns that the increase in fees to up to £9,000 per year will deter students from staying on for further postgraduate qualifications.

At earlier debates in Oxford about the fee increase, academics had warned that this could narrow the intake of future postgraduate students and the next generation of academics.

Prof Hamilton said that the lack of funding could mean that the most talented graduates could be lost to other countries.

"There are sadly too many examples of Oxford losing bright graduate students to overseas universities because of the funding gap. It is the single biggest reason why those to whom we make offers turn us down," he said.

Prof Hamilton also said the arguments about universities supporting social mobility would sound "increasingly hollow" if there were financial barriers for students wanting to stay for postgraduate courses.

"It is surely time, as we have urged, for a fresh look by policy makers. It is striking for example that there is nothing in the UK to compare with the US government's federal loans scheme, to enable graduate students to finance their study."

Last week, Harvard consolidated its position as the wealthiest university in the world, reporting that its endowment has risen in value to £21bn.

The endowment provides about a third of the university's operating budget, which last year was £2.4bn.

In comparison, the University of Oxford last year had an income of £880m.