Allen was born in Battersea, London, in 1894, married Aleta Cosette Turner in Leeds in 1926 and died in Easebourne, West Sussex, in 1982.

Serving in Flanders in the First World War, he made friends with Bud Flanagan, but they did not work together until 1926, touring with a Florrie Forde show called "Here's to You".

Flanagan and Allen's songs featured the same, usually gentle humour for which the duo were known in their live performances, and during the war reflected the experiences of ordinary people during wartime.

Other songs such as their best-known "Underneath the Arches" (which Flanagan co-wrote with Reg Connelly) had universal themes such as friendship, which, again, helped people relate to the subject matter.

Flanagan and Allen stopped performing together with Chesney Allen's retirement on health grounds in the late 1950s following the penultimate season of the Crazy Gang's show at the Victoria Palace Theatre in London (his place for the final season was taken by 'Monsewer' Eddie Gray), although he continued working in theatrical management and returned to make occasional guest appearances.