The Peyton baronetcy, of Doddington in the County of Cambridge, was created for the third time on 18 September 1776 for Henry Dashwood, son of Margaret Peyton, daughter of Sir Sewster Peyton, 2nd Baronet of the second creation. Dashwood, who was related to the Dashwood baronets changed his name by Act of Parliament to Henry Dashwood Peyton. The 1st and 2nd Baronets sat as MPs for Cambridgeshire in 1782 and 1802 respectively.
From the time of the 2nd Baronet, the family had a seat at Swift's House, Stoke Lyne, Oxfordshire. The 2nd Baronet served as High Sheriff of Cambridgeshire and Huntingdonshire for 1808 and the 4th, 5th, 6th and 7th Baronets served as High Sheriff of Oxfordshire for 1871, 1881, 1896 and 1928 respectively.
The baronetcy became extinct on the death of the 7th Baronet in 1962.