Born in Kilmarnock. Met Robert MacBryde, a year his senior, at the Glasgow School of Art in 1933. They moved to London in the early years of the Second World War and in the post-war period became two of the most influential artists of their generation. The London art world found them to be successors to Graham Sutherland, Henry Moore and Ben Nicholson, alongside their friends Francis Bacon and Lucien Freud. On Alfred Barr's visit to London in 1948, while director of the Museum of Modern Art, New York, he went searching for the best contemporary British art to take back for his personal collection in the US. He returned with works by Colquhoun, MacBryde, Bacon, Edward Burra and Freud, which he displayed together. 'The Two Roberts'.
Colquhoun had his first solo show at the Lefevre Gallery in June 1943, which featured twenty-six paintings, one of which was bought by Sir Kenneth Clark. The Two Roberts held a joint exhibition of paintings at the Gallery in October 1944, in which Colquhoun is recognised to have developed to his early-mature style and he was dubbed 'Master of the Female Half-Length' (Stephen Bone, Manchester Guardian, 1958). Many of his paintings from this period are brooding with deep ochres, a palette which has been ascribed to his habit of painting at night under artificial lighting.
A major retrospective of the work of Colquhoun and his partner Robert MacBryde, known as the two Roberts, was held at the Scottish National Gallery of Modern Art in Edinburgh in 2014-15.