He was not yet two years old when his father died, so he was raised by his uncle William Singleton (d. 1793), who had studied under the tutelage of Ozias Humphry and painted portraits and miniatures.
Henry Singleton died in London at the age of 72, at the house of a friend at 7 Kensington Gore, and was buried in the church of St Martin-in-the-Fields.
He exhibited at the Royal Academy, between 1784 and 1839, approximately 300 works, a large proportion of which were portraits, with scriptural subjects making up much of the remainder.
Early in his career, Singleton was noted for large compositions from the Bible, Shakespeare or contemporary historical events.
Paul I Granting Liberty to Kościuszko (1797) and The Death of Captain Alexander Hood after Capturing the French 74 "L'Hercule", 21 April 1798 are considered by some to be his best works.