The son of the Conservative politician Alexander Staveley Hill, Hill (who assumed by Royal Licence the name of Staveley in 1906) was educated at Westminster School and St John's College, Oxford, where he rowed for the college. He was called to the bar at the Inner Temple in 1891, and practiced on the Oxford circuit.
Following in the steps of his father, he became first Recorder of Banbury (1903–22) and Conservative Member of Parliament for Kingswinford (1905–18). During the First World War, Staveley-Hill commanded the 2/1st Staffordshire Yeomanry, with the rank of lieutenant-colonel, then became Superintending Officer, Labour Corps, Scottish Command.
Staveley-Hill was appointed a County Court judge in 1918. He resigned in 1928, after an order in bankruptcy had been made against him.
- "His Honour H. S. Staveley-Hill". The Times. 26 March 1946. p. 6.
- Hansard 1803–2005: contributions in Parliament by Henry Staveley-Hill