Henry Singleton was born in London, England, into an artistic family. 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. Another uncle, Joseph Singleton, exhibited at the Royal Academy between 1773 and 1788. Henry’s sisters Maria and Sarah (later Macklarinan) were miniaturists who exhibited at the Royal Academy from 1808 to 1820 and from 1787 to 1806 respectively.
In 1807 Henry married his cousin William Singleton’s only daughter.
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.