[1] He had an elder brother, John,[2] a fellow classicist, who taught Classics at The King's School, Peterborough, and a sister, Avril.

[2][5] After leaving school, Dexter completed his national service with the Royal Corps of Signals and then read classics at Christ's College, Cambridge, graduating in 1953 and receiving a master's degree in 1958.

[5] In 1954, Dexter began his teaching career as assistant Classics master at Wyggeston Grammar School for Boys in Leicester.

Last Bus to Woodstock was published in 1975 and introduced the character of Inspector Morse, the irascible detective whose penchants for cryptic crosswords, English literature, cask ale, and music by Wagner reflected Dexter's own enthusiasms.

Dexter's plots used false leads and other red herrings,[11] "presenting Morse, and his readers, with fiendishly difficult puzzles to solve".

[12] The success of the 33 two-hour episodes of the ITV television series Inspector Morse, produced between 1987 and 2000, brought further attention to Dexter's writings.

A prequel series, Endeavour, features a young Morse and stars Shaun Evans and Roger Allam.

Endeavour was first broadcast on the ITV network in 2012, ending with the ninth series in 2023, taking young Morse's career into 1972.