Brookshaw was born in Southwark, in London, and educated at the Central School of Arts and Crafts. He was a particularly accomplished lithographer, skilled also as a painter in both oil and watercolour. Identifying the former talent, F Gregory Brown – the poster and textile designer – encouraged him to become an illustrator and poster designer. Producing posters for London Transport and Shell, inter alia, between 1928 and 1958, many of his posters depict sporting events. His two posters for the annual University Boat Race are well known and highly sought after, and his wonderful posters often evoke a feeling of movement, whether rowers straining on their oars, or horses or greyhounds racing.