Born in Wingfield near Chesterfield, Derbyshire, Greatorex as a youngster studied with Benjamin Cooke, organist of Westminster Abbey, and was a protégé of the Earl of Sandwich.
For four years he was organist of Carlisle Cathedral and from there went to live and work in Italy, where he became a friend of Charles Edward Stuart, or "Bonnie Prince Charlie."
When the Young Pretender died in 1788, he left some of his music books to Greatorex, who returned to London the same year.
[2] From 1771, Anthony was organist at St Modwen's, Burton upon Trent, in which role Thomas succeeded him.
One of these, Henry Wellington Greatorex, became a church organist in Hartford, Connecticut, United States, and composed many hymns.