Allen was born in Portsmouth in 1939, as Trevor Abbott. He adopted his stepfather’s surname, Allen.
After national service in the Royal Anglian Regiment – spent partly in Libya – he studied from 1960 to 1964 at the Camberwell School of Arts and Crafts. During these years he worked with Michael Rothenstein at his studio in Great Bardfield, Essex, where there was a significant artistic community. He was also a studio printer with Editions Alecto, a pioneering print publisher which had been set up in a former factory for non-alcoholic communion wine in Kelso Place in Kensington. In 1964 Allen set up a print studio for himself in Balham.