Carpenter was born, died, and lived practically all of his life, in the city of Oxford. His father was Harry Carpenter, Bishop of Oxford. His mother was Urith Monica Trevelyan, who had training in the Fröbel 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. He was educated at the Dragon School Oxford, and Marlborough College, and then read English at Keble.
His notable output of biographies included: J. R. R. Tolkien: A Biography (1977; also editing of The Letters of J. R. R. Tolkien), The Inklings: CS Lewis, JRR Tolkien, Charles Williams and their Friends (1978; winner of the 1978 Somerset Maugham Award), W. H. Auden (1981), Ezra Pound (1988; winner of the Duff Cooper Memorial Prize), Evelyn Waugh (1989), Benjamin Britten (1992), Robert Runcie (1997), Dennis Potter and Spike Milligan (2004). His last book, The Seven Lives of John Murray (2008) about John Murray and the famous publishing house of Albemarle Street, was published posthumously.
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. The Joshers: Or London to Birmingham with Albert and Victoria (1977) is a children's adventure book, similar in style to The Railway Children and based on the adventure of taking a working narrowboat up the Grand Union Canal from London to Birmingham. His encyclopaedic work The Oxford Companion to Children's Literature (1984), written jointly with his wife, has become a standard reference source.
A distinguished broadcaster, he began his career at BBC Radio Oxford as a presenter and producer where he met his future wife, Mari Prichard (whose father was Caradog Prichard, the Welsh novelist and poet); they married in 1973. They jointly produced A Thames Companion in 1975. He played a role in launching Radio 3's 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 poet Robert Burns, the major focus of her creative work. BBC Radio 4 broadcast this programme on New Year's Eve, 2004.
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. 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.
His death was the result of heart failure, compounded by the Parkinson's disease from which he had suffered for several years. A commemorative stained glass window has been installed in St. Margaret's Institute, Polstead Road honouring Carpenter's many accomplishments. He is survived by his wife, and daughters Clare and Kate.