Coulson was born in Kilburn, London, his father being a columnist for The Sunday Chronicle. Leslie and his brother attended boarding school in Norfolk, and Leslie then worked as a reporter on the Evening News. He joined the Royal Fusiliers in 1914 and saw service in Malta, Egypt and Gallipoli, before arriving at the Western Front in 1916.
His collected poems were published posthumously in 1917, edited by his father, and sold 10,000 copies in the first year. The best known of the poems is "Who Made the Law?"