The trust found the number of pupils at the top 30 comprehensives who went to Oxbridge was just a third of what might be expected if based on ability.
But at the top 30 independent schools, more than expected got Oxbridge places.
The Sutton Trust is committing at least £10m over the next five years to lift the chances of youngsters from disadvantaged backgrounds.
It wants others to "join the cause", both financially and by coming up with innovative schemes.
It is also investigating how it can help state schools where the average A-level (or equivalent) score is high but the access to the top universities is relatively low.
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