Paxton was descended from a Berwickshire family with a tradition of service in the Presbyterian ministry. His grandfather John Paxton, a burgess of Edinburgh, was employed there for many years by Archibald Stewart†, a wealthy wine merchant and Member for the city, and later became a partner in the business which Stewart transferred to London in 1747. His father Archibald assumed sole control of the firm in the early 1780s and later formed a partnership with Stewart Marjoribanks*, a grandson of Archibald Stewart, who had married his illegitimate daughter Eleanor; he married the daughter of an ‘immensely rich’ partner in the London stationary business of Wright, Gill and Dalton of Abchurch Lane, purchased an estate at Watford and served as sheriff of Hertfordshire in 1799.
He was an occasional attender who gave general but silent support to Lord Liverpool’s ministry. He divided against Catholic claims, 28 Feb., repeal of the additional malt duty, 3 Apr., parliamentary reform, 9 May, and abolition of the death penalty for forgery, 23 May 1821. He voted against more extensive tax reductions, 11 Feb., abolition of one of the joint-postmasterships, 13 Mar., removal of Catholic peers’ disabilities, 30 Apr., and for the aliens bill, 19 July 1822. He divided for the Irish glebes grant, 11 Apr., and against repeal of the Foreign Enlistment Act, 16 Apr., and inquiries into the prosecution of the Dublin Orange rioters, 22 Apr., and delays in chancery, 5 June 1823. He voted for the Irish insurrection bill, 14 June 1824, and the Irish unlawful societies bill, 25 Feb., and against Catholic claims, 1 Mar., 21 Apr. 1825. He voted in the minority for the Leith docks bill, 20 May, but with government for the duke of Cumberland’s annuity, 10 June 1825. He retired from Parliament at the dissolution in 1826. He served as sheriff of Dorset in 1828 but sold out of the county two years later.
