Satire/Comedy
The book's a traditional comedy in the sense that it's humorous and it gives Jim a happy ending with his new girlfriend, Christine (courtesy of his fairy godfather, Mr. Gore-Urquhart). But the book is primarily a satire, as it ruthlessly makes fun of universities as places of eccentric, self-absorbed people engaged in trivial and worthless pursuits.
But Kingsley Amis isn't just concerned with mocking the university system. He's at his funniest ridiculing the types of people that you'd be likely to meet in a British university town in the 1950s: pretentious arty types like Bertrand; the absent-minded Professor Welch with his head in the clouds and the Middle Ages; the sycophant (suck-up) Mr. Michie; the academic fraud Caton; the pretentious Principal who tries to curry favor with rich potential donors. You can just tell that Amis has met all of them.