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Sir Henry Dashwood Peyton, 1st Baronet (1736–89), of Doddington, Cambridgeshire, was an English politician.
He was born the eldest son of George Dashwood and succeeded his uncle in 1771, taking the latter's name of Peyton as his own. He inherited land at Doddington in Cambridgeshire and Narborough Hall in Norfolk, was created a baronet in 1776, and pricked High Sheriff of Norfolk in 1778.
He was a Member (MP) of the Parliament of Great Britain for Cambridgeshire 20 June 1782 to 1 May 1789.
He married Frances, the daughter of Sir John Rous, 5th Baronet and had 2 sons and 3 daughters. He was succeeded as baronet by his eldest son, Sir Henry Peyton, 2nd Baronet. His daughter, Harriet Peyton, married Thomas Kingscote (b. 9 Dec 1757, d. 15 Apr 1811) on 8 October 1794.