Stanley, who was blind from an early age, studied music with Maurice Greene and held a number of organist appointments in London. He was a friend of George Frideric Handel, and following Handel's death, Stanley joined first with John Christopher Smith and later with Thomas Linley to continue the series of oratorio concerts Handel had established.
In 1779, Stanley succeeded William Boyce as Master of the King's Musick.
Stanley's works include the opera Teraminta, the dramatic cantata The Choice of Hercules, twelve other cantatas with texts by John Hawkins, the oratorios Jephtha, The Fall of Egypt and Zimri, and instrumental music.