Colquhoun was born in Kilmarnock. He studied at Glasgow School of Art from 1933 to 1938, where he met Robert MacBryde. The two immediately formed a close friendship and became known as 'the two Roberts'. In 1944 they moved to London, where they were drawn into the Neo-Romantic group, finding a studio which they shared with the painter John Minton. By the mid-1940s Colquhoun's style had turned towards a bleak, almost existential view of the world. His famously boisterous lifestyle earned him a reputation which often threatened to eclipse his art.