Sir Richard also urged public funding for private schooling
One of the UK's most prestigious universities may use its own entrance exam to differentiate between well-qualified degree applicants.
Imperial College London is trying out an entrance test for subjects other than medicine, which has one already.
Rector Sir Richard Sykes told an independent schools conference that all applicants had "four or five A-levels".
He said it was "frightening" that 40% of his undergraduate intake came from
the 7% who were privately schooled.
Imperial specialises in engineering, medicine, and the natural sciences and was ranked fifth in a recent global league table.
Speaking at the Independent Schools Council's annual conference in London, Sir Richard said "grade inflation" had "destroyed" the role of A-levels in selecting undergraduates.
"Top institutions have great difficulty separating out the best students," he said.
"Even if you interview all the students you still have a problem."
Hence the trials of an entrance test to assess general intelligence and creativity, which could become the norm at Imperial from 2010 and perhaps elsewhere.
"That hopefully would become a national system if that was seen to be successful for selecting students," Sir Richard said.
"We are doing this not because we don't believe in A-level but we cannot use A-levels any more as a discriminatory factor. They have all got four or five A-levels," he said.
A-levels and other suitable qualifications will still be required as well.
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A-levels are so devalued, universities should set their own entrance exams
Steps have been taken to make A-levels more demanding, partly in response to concerns that so many students now achieve A grades, making it difficult to distinguish between the good and the very good.
Among other things a top A* grade is being introduced to address this issue.
In recent years some universities have begun using entrance exams for specific subjects such as medicine and law.
Sir Richard also made a wider attack on the state of education in the UK.
"We have got to do something radical if we are going to save children in 93% of our schools that somehow are just not getting the education they deserve," he said, referring to the proportion in state schools.
"We have in this country some of the best secondary education in the world but only a few percentage of people benefiting from it."
He said radical action was needed to "save" bright children by taking them out of state schools and using public funding to support them in private schools.