Singleton was born in London. While Henry was young his father died. Assisted in his ambitions to be an artist by his uncle, the miniaturist, William Singleton, Henry entered the Royal Academy Schools in 1783. He exhibited prolifically at the Royal Academy from the age of eighteen until his death. He made a number of portrait paintings but he was mainly employed as a book illustrator, working in the manner of Wheatley. Redgrave notes that towards the end of his life, Singleton completed a series of small-sized pictures from Shakespeare.