Whalley was born Allan Mark Whalley in 1961 in Burnley, Lancashire. Before joining Chumbawamba he attended Art College in Maidstone and worked in a supermarket and as a postman. His parents were both primary school teachers.
Together with his fellow members of Chimp Eats Banana, Midge and Danbert Nobacon, he moved to Leeds in 1981 and studied at the University of Leeds, dropping out after a year before moving into the South View House squat in Armley. He became a guitarist despite describing himself as being of "limited ability". He continued to play guitar and sing while doing a series of other jobs such as shopworker, newspaper delivery man, typesetter, and cartoonist.
The name Boff came from being nicknamed "College Boffin" by other workers at the Supasave supermarket in Burnley, where Whalley worked after leaving school. Whalley's first band Chimp Eats Banana had a song called "Supasave".
Beyond his musical career, Whalley has been prominent in the fell running scene, particularly in West Yorkshire, running at a relatively high standard. Touring and recording commitments have influenced the extent to which he has been able to pursue this activity. He was instrumental in the production of the Fellternative fell running fanzine in the early 1990s.