Oxford University should be able to charge unlimited fees to maintain its elite status, its chancellor has said.
Lord Patten said public school "yobs" made recruitment difficult
Chancellor of Oxford, Lord Patten, said that if the university did not charge higher fees it would struggle to compete internationally.
In a speech at Green College he said he hoped fees would be uncapped by 2030.
But Lord Patten did admit Oxford had "a problem" with attracting students from poorer backgrounds due to the behaviour of public school "yobs".
"It cannot be very good for recruitment of able sixth formers in Yorkshire comprehensives when a bunch of yobs with more money than sense do what young yobs have always done and always will do.
"That is to behave in ways that shame the families and schools that have lavished advantages on them."
Research from the Sutton Trust suggests 3,000 students with excellent A-Levels from less wealthy backgrounds do not apply to the country's best universities every year.
He said Oxford ranked highly in international comparisons and Britain had the second best universities in the world - after the US.
But he warned that without more money, from the Government, industry and donations from former students, Oxford would struggle.
"We are still in the race, but there is not much petrol left in the tank," he said. "Can we be world-class - can anyone be - without being privately funded as well as an independent institution, like the Ivy League universities?"
Last week, Oxford published a strategy paper which said it cost £18,600 a year to educate the average Oxford undergraduate - but the university only received a total income of £9,500.
From next year, most universities will charge top-up tuition fees of £3,000 a year - but Lord Patten said this would not be enough in the long-term.