Speaking at a debate on Oxbridge and social mobility at the Battle of Ideas festival in London last week, Richard Partington, who is also the senior tutor at Churchill College, Cambridge, disputed a fellow panellist's claim that the quality of secondary education had declined.
"I would really struggle to find colleagues who disagreed with me," he said regarding the improvement in students.
He also defended the rigour of A levels, arguing that they were a "really excellent predictor of how people will do at university".
In 2009-10, 59.3 per cent of young first-time degree entrants at Cambridge came from state schools. The proportion at the University of Oxford was 54.3 per cent.
Mr Partington said that the figure at Cambridge should be 65 per cent because this was the proportion of top A-level results achieved by state school pupils.
He said Cambridge's outreach efforts were partially self-interested because the university wanted to find the best students: "We will be getting the best when we're recruiting 65 per cent state school pupils." Using a racing car metaphor, he said: "You need to go out and get the best fuel you can and stick it in the engine."
However, on the more general point about social mobility, he said that raising the proportion of state school-educated students at Cambridge above 65 per cent, based on current A-level results, would require positive discrimination.
Mr Partington explained that the number of state school pupils at the university "fell off a cliff" after 1981, plummeting from about 70 to 40 per cent and beginning to improve only after 1997. "In the end, the main reason is educational achievement in schools," he said.