Tomlinson was born in Rawtenstall, Lancashire, England, into a musical family, one of four children to Fred Tomlinson Sr and May Tomlinson (née Culpan). His younger brother, Fred Tomlinson, also a musician, founded The Fred Tomlinson Singers and performed the music for "Monty Python's Flying Circus". At the age of nine he became a chorister at Manchester Cathedral, where he was eventually appointed as Head Boy in 1939. He later attended Bacup and Rawtenstall Grammar School and at sixteen won a scholarship to Manchester University and the Royal Manchester College of Music. He spent the next two years studying composition until in 1943 he left to join the Royal Air Force, where, although colour-blind, he became a wireless mechanic and saw service in France during 1944 and 1945. He returned to England in 1945 to resume his studies and graduated in 1947, receiving the degree of Bachelor of Music for composition as well as being made a Fellow of the Royal College of Organists and an Associate of the Royal Manchester College of Music.