Montgomery was educated at Merchant Taylors' School and graduated from St John's College, Oxford, in 1943, with a BA in modern languages, having for two years been its organist and choirmaster. From 1943 to 1945 he taught at Shrewsbury School. He first became established under his own name as a composer of vocal and choral music, including An Oxford Requiem (1951), but later turned to film work, writing the scores for many British comedies of the 1950s, most notably the Carry On series. He composed six scores for Carry On producer Peter Rogers including the original Carry On theme subsequently adapted for later films by Eric Rogers. Montgomery was responsible for both the screenplay and score of Raising the Wind (1961).

His novels feature the Oxford don Gervase Fen, who is the Professor of English at the university and fellow of St Christopher's College, a fictional institution that Crispin locates next to St John's College. Fen is an eccentric, sometimes absent-minded, character reportedly based on the Oxford professor W. E. Moore. The whodunit novels have complex plots and fantastic, somewhat unbelievable solutions, including examples of the locked room mystery. They are written in a humorous, literary and sometimes farcical style and contain frequent references to English literature, poetry, and music. They are also notable for being among the few mystery novels to break the fourth wall occasionally and speak directly to the audience. Perhaps the best example is from The Moving Toyshop, during a chase sequence -- "Let's go left," Cadogan suggested. "After all, Gollancz is publishing this book."

Gareth Roberts has stated that the tone of his Doctor Who novel The Well-Mannered War was modelled upon Crispin's style. He also remarks (of The Moving Toyshop) that "It's more like Doctor Who than Doctor Who." Novelist Christopher Fowler pays homage to The Moving Toyshop in The Victoria Vanishes, his sixth Bryant & May novel. Crispin is considered by many to be one of the last great exponents of the 'classic' crime mystery. BBC - Doctor Who - Classic Series - Ebooks - Introduction - Let me entertain you

Montgomery's output of music and fiction all but ceased after the 1950s, but he continued to write reviews of crime novels and science fiction works for The Sunday Times. Alcoholism was a factor in his early death from a heart attack.

A biography by David Whittle, Bruce Montgomery/Edmund Crispin: A Life in Music and Books (ISBN 10: 0754634434) was published in June 2007.

• The Case of the Gilded Fly (1944)
• Holy Disorders (1945)
• The Moving Toyshop (1946) was dedicated to Crispin's great friend and fellow admirer of the work of John Dickson Carr, Philip Larkin.
• Swan Song (1947)
• Love Lies Bleeding (1948)
• Buried for Pleasure (1948)
• Frequent Hearses (1950)
• The Long Divorce (1952)
• Beware of the Trains (1953) (short story collection)
• The Glimpses of the Moon (1977)
• Fen Country (1979) (short story collection, published posthumously)

Crispin also edited seven volumes entitled Best Science Fiction, which were published during the 1960s .