Sir Henry Peachey, 1st Baronet (c. 1671–1737), of New Grove, Petworth, Sussex, was a British landowner and Whig politician who sat in the House of Commons in three periods between 1701 and 1737.
At the second general election of 1701 he was returned in a contest as Whig Member of Parliament for Sussex.
[3] Peachey applied to the Duke of Newcastle for support as a prospective candidate for Sussex at a by-election in 1728, but was not adopted.
He was created baronet on 21 March 1736, with a special remainder to his brothers John and James.
Shortly after, he was returned as MP for Midhurst in a by-election on 2 February 1736 in succession to his brother, Bulstrode Peachey Knight.