He insisted ministers were not interfering, but added: "Universities should support students from poorer backgrounds and reach out to the largest pool of young people."
Asked whether universities would resent turning to business for extra funding, Mr Lammy said: "I hope not. They are already doing this on low-carbon technologies, engineering, IT and the health service."
Sir Howard Newby, Liverpool University's vice-chancellor, insisted it was "renowned for its track record in widening participation", spending £6m a year on scholarships.
But he insisted: "Academic achievement continues to be the key factor in determining whether a student will go on to university."
Sir Howard said it was wrong to measure the quality of a course according to the number of "contact hours", although Liverpool was providing more of that information.
And he insisted extra income from industry and philanthropy could not solve universities' funding problems.
