He was born in the Newington Green area of Islington, London, England, into a Roman Catholic household. He was brought up in Luton and Bristol. After school he worked as a bus conductor and civil servant before attending the University of Bradford, where he gained a B.Sc. in European Literature and the History of Ideas and Sociology.

Hegley has French ancestry (his father's name was René) and he claims to be a descendant of the composer Jean-Philippe Rameau. His paternal grandmother was a dancer with the Folies Bergère.

Hegley began his performing career at London's Comedy Store in 1980, and received national exposure when he appeared with his backing band the Popticians on Carrott's Lib in 1983, and recorded two sessions for John Peel in 1983 and 1984. Hegley published his first poetry collection, Visions of the Bone Idol (Poems about Dogs and Glasses), pieces from which were later incorporated into Glad to Wear Glasses, in 1984.

Hegley has written a number of collections of poetry, ranging from the surreal through the humorous to the personal and emotional. There are a number of recurring themes in his poems, notably glasses, dogs and reminiscences of his childhood in Luton.

He was presenter of the Border Television series Word of Mouth - in which numerous contemporary poets performed their work - in 1990, and the BBC radio series Hearing with Hegley from 1996 to 1999. His other television appearances include Wogan and Never Mind the Buzzcocks.

In 1998, Hegley's poem "Malcolm" came second in a BBC survey to find Britain's most popular comic poem.

In 1999 he starred in a Simon Callow-directed revival of the musical The Pajama Game in London's West End.

The University of Luton awarded him an honorary LL.D. in 2000, and he has also led creative writing courses at the university.

Hegley frequently performs live and is a regular at the Edinburgh Festival. His stage act includes elements of poetry, music (he plays the mandolin and is often accompanied by a double bassist), comedy and Luton Town Football Club. He also likes to utilise audience participation in his shows, for example by having a dog drawing competition during the interval, or by asking his audience to try writing poetry themselves.