Carpenter was born, died, and lived practically all of his life, in the city of Oxford. His father was the Rt. Rev. Harry James Carpenter. His mother was Urith Monica Trevelyan, who had training in the Froebel teaching method. As a child, he lived in the Warden's Lodgings at Keble College, Oxford, where his father served as Warden until his appointment as Bishop of Oxford. On leaving the Dragon School in Oxford, Humphrey studied at Marlborough College in Wiltshire, but returned to study English at Keble. During his appointment at BBC Radio Oxford, Humphrey met his future wife, Mari Prichard (whose father was Caradog Prichard, the Welsh novelist and poet); they became married in 1973. His notable output of biographies included: J. R. R. Tolkien (1977) (also editing of The Letters of J. R. R. Tolkien), The Inklings (1978), W. H. Auden (1981), Ezra Pound (1988), Evelyn Waugh (1989), Benjamin Britten (1992), Robert Runcie (1997), and Spike Milligan (2004).
He also wrote histories of BBC Radio 3 (on which he had regular stints as broadcaster), the British satire boom of the 1960s, Angry Young Men: A Literary Comedy of the 1950s (2002), and a centennial history of the Oxford University Dramatic Society in 1985. His Mr Majeika series of children's books enjoyed considerable popularity and were successfully adapted for television. His encyclopedic work The Oxford Companion to Children's Literature (1984), written jointly with his wife Mari Prichard, has become a standard reference source.
A distinguished broadcaster, he began his career at BBC Radio Oxford as a presenter and producer before moving to national radio. He played a vital role in launching Radio 3's ongoing arts discussion programme Night Waves and acted as a regular presenter of other programmes on the network including Radio 3's afternoon drivetime programme In Tune and, until it was discontinued, its Sunday request programme Listeners' Choice. Until the time of his death, he presented the BBC Radio 4 biography series Great Lives recorded in Bristol. The last edition recorded before his death featured an interview with the singer Eddi Reader about the Robert Burns, the major focus of her creative work. BBC Radio 4 broadcast this particular programme on New Year's Eve, 2004. In 1983, he formed a 1930s style jazz band, Vile Bodies, which for many years enjoyed a residency at the Ritz Hotel in London. He also founded the Mushy Pea Theatre Group, a children's drama group based in Oxford, which premiered his Mr. Majeika: The Musical in 1991 and Babes, a musical about Hollywood child stars. Carpenter's other abilities included being a talented amateur jazz musician and an accomplished player of the piano, the saxophone, and the double-bass, playing the last instrument professionally in a dance band in the 1970s. His early death was the result of heart failure, compounded by the Parkinson's disease from which he had suffered for several years. His survivors included his wife, and daughters Clare Carpenter and Kate Carpenter.