The son of a country gentleman of Wiltshire, Hill was educated at Westminster School, and afterwards travelled in the East.
Having written some satiric lines on Alexander Pope, he received in return a mention in The Dunciad, which led to a controversy between the two writers.
Hill was the manager of the Theatre Royal, Drury Lane when he was 24 years old, and before being summarily fired for reasons unknown, he staged the premier of George Frideric Handel's Rinaldo, the first Italian opera designed for a London audience.
The composer was very involved in the production, and Hill collaborated on the libretto, although it is disputed what his actual contributions were.
His biography was recorded in Lives of the Poets of Great Britain and Ireland, to the Time of Dean Swift, volume 5 (ostensibly by Theophilus Cibber but generally accepted to be of anonymous authorship).