Henry Cressett Pelham (1729? – January 1803) was a British politician, known as Henry Pelham until 1792. The youngest son of Thomas Pelham, he was educated at Corpus Christi College, Cambridge, and became a fellow of Peterhouse in 1751. In the same year, he was returned for Bramber as a Government supporter; the electoral patronage there was leased by Lord Archer from Sir Henry Gough, who controlled it. In the 1754 election, he was instead returned for another government borough, Tiverton in Cornwall.