British universities are suffering from a malaise, I suggested recently in the latest edition of The Good Schools Guide. My particular focus was the rising number of British students rejecting narrow courses in UK universities for wider alternatives in the US. "Storm in a teacup" has been the typical response from those running universities here, who view those quitting these shores as predominantly middle-class students in search of an easy ride.

This reaction is understandable but it is wrong. More than 10,000 British applicants sat the main admissions test for entry to US universities last year, up a third on 2008 levels. Generous bursaries in US universities make it possible for UK students to attend, even if they have very limited means. Dismissing these students as superficial rich kids is belittling and complacent.

Take one of my students, Felix Cook, who recently rejected his Oxbridge place for Harvard University. He finds its intellectual quality and the challenge of academic stretch beyond his core subject hugely rewarding.

"My school taught me about education for life and becoming a rounded individual," he told me. "The Oxbridge focus seemed to be only on exam results."

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Cook may well have had a better time at Oxbridge, but his thoughts merit attention.

Let's get this straight. I'm not slagging off British universities, which in most important ways are doing a tremendous job. To have three of them in the top 10 of the Times Higher Education World University Rankings - the University of Oxford (fourth), the University of Cambridge (sixth) and Imperial College London (eighth) - is a source of huge pride. Only the US academy, with its vastly greater resources, beats the UK on the world stage. If we take THE's 100 Under 50 table, the UK again does extraordinarily well, with five institutions in the top 20: the University of York (eighth), Lancaster University (ninth), the University of East Anglia (10th), the University of Warwick (13th) and the University of Essex (20th). Overall, we have more institutions in the rankings than any other nation (20).

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Our spending on undergraduates is another cause for celebration. Not for a generation has so much been spent per capita on UK students as will be the case in 2012-13. Much, of course, will depend on how UK universities choose to spend the money, but they have the opportunity to channel it in productive ways to enrich the student experience.

Some have been successful innovators. Oxford has put considerable thought and imagination into ways to enhance its teaching. Loughborough University has an award-winning maths clinic. The University of Hertfordshire has made links with local businesses part of the experience of every undergraduate. The University of Southampton created the National Oceanography Centre in 2010, integrating marine science and technology in a novel way. And University College London, with its "grand research challenges", is doing innovative cross-disciplinary work.

But for all this, complacency remains a serious problem. The brilliance and originality of many of our academics is not matched by those responsible for university strategy, which is often conservative, defensive and reactive.

The world is changing dynamically. Challenges are coming not just from the US but increasingly from East Asia and India. Digital technology and new providers are calling into question the future financial viability of residential higher education.

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Our universities are often first class on research but not on teaching, especially of the arts, as surveys reveal. Some institutions such as the University of Manchester have responded quickly to dissatisfaction; others have not.

Our three children have loved studying arts degrees, but one of our daughters complained that her philosophy and sociology teaching was ad hoc and lacked commitment, while our son is bitterly disappointed at having only two essays a term in history.

"My friends at Oxbridge are doing an essay a week," he says. "They are forging ahead of me intellectually." They speak for many.

Beyond academic study, too little attention is paid to student well-being and to the breadth of the student experience: cheap alcohol is no substitute for lack of pastoral care or stimulus. The understanding of schools is patchy (which explains the continued love affair with sat-nav A levels rather than the far more profound intellectual learning of the International Baccalaureate). Courses are often far too narrow. The liberal-arts degrees found in the US are rightly popular - and are being emulated by A.C. Grayling's New College of the Humanities.

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The insularity of many institutions is highlighted by their unwillingness to follow the example of UCL and the universities of Nottingham and Liverpool and open branches abroad. Foreign governments, such as those of China and Malaysia, belittle UK institutions because of their reluctance to engage, in stark contrast to their US peers. No British university except Oxbridge has yet managed to become a global brand. Our academy is still one of the best in the world, but it needs to change.