The "hippo" of the title (occasionally referred to as "the happy hippo" and given to wallowing in long baths) is Edward (Ted/Tedward) Lennox Wallace, an aging, lecherous, one-time hell-raising poet, reduced by diminishing poetic talent to working as a theatre critic. The story opens with the aftermath of Ted being sacked from his job on a newspaper.
At the suggestion of a sick goddaughter, Jane (suffering from leukemia), he goes to stay at the Norfolk country house of old schoolfriend and Army colleague from National Service, Lord Michael Logan and his wife Lady Anne, to investigate unspecified mysterious goings-on.
Ted reports back to Jane regularly, in the form of long, rambling letters, apprising her of events at Swafford Hall whilst also offering his views on numerous other issues (women, art, poetry, sex, morality and modern life being favorite topics), all the time attempting to uncover the nature of the unusual events that Jane has instructed him to look out for.
Over the course of his stay it gradually becomes apparent that other house guests are ascribing healing powers to one of Logan's children, David (Ted's other godchild), and indeed it is in the hope that he might bestow his "talent" upon them that they have descended upon Swafford Hall. Amongst the assembled guests are a witty and hugely camp, but rebarbative defrocked minister and TV producer, a businessman and his wife and rather gawky teenage daughter, a friend of Jane's, and Jane's mother - a woman Ted has crossed paths with disastrously many years earlier.
The life stories of the tycoon Logan and his family, as well as Ted's own, are intertwined to provide a colourful and credible back story. The highly comical story is run through with a stream of sexual practices, some more unusual than others, as Ted uncovers the means by which David delivers his "healing."