Barton was commissioned lieutenant on 6 June 1776 and promoted commander of the cutter Bustler 14 on 6 November 1782, which vessel he commissioned for service in the Irish Sea, operating out of Holyhead. Having arrived at Portsmouth on 26 May 1786, his command was paid off shortly afterwards.
In early August 1793 he was appointed to the newly launched sloop Hawke 16, which on 8 November in company with the frigates Quebec 32, Captain Josias Rogers, and Pomona 28, Captain Henry d’Esterre Darby, arrived at Portsmouth with troops from Ostend that were to join Vice-Admiral Sir John Jervis’ Leeward Islands campaign. She later sailed from Deal on 6 November to collect a convoy from Ireland, and she was back off the Isle of Wight towards the end of January 1794 before returning to the Downs where she remained stationed for some weeks.
Barton was posted captain on 2 April 1794, and in July recommissioned the nine-pounder frigate Lapwing 28 following her extended refit at Woolwich. In the early summer of 1795 he escorted a convoy from the Thames and Humber to Elsinore, arriving in mid-May, and by August his command was lying windbound in the Leith Roads with a troop convoy before eventually putting out that month. She then saw service in the North Sea fleet under Admiral Adam Duncan.
On 4 October 1795 the Lapwing departed Spithead for the Humber to collect transports for the embarkation of troops for the Caribbean, and after sailing for the Leeward Islands she remained stationed there. On 25 November 1796 she left St. Kitts for Anguilla upon being informed of a French landing on that island, and her arrival the next day saw one enemy vessel, the Décius 20, captured within the hour having suffered one and hundred and twenty casualties, equating to a third of her crew, whilst a second vessel, the brig Valliante 10, ran herself ashore to avoid capture and was destroyed by cannon fire. The Décius was found to be damaged beyond repair and was destroyed the next day, but the French incursion had at least been defeated. During this operation Barton’s command suffered one man killed and six wounded, and as a reward for it’s’ success his first lieutenant was promoted master and commander by Earl Spencer, the first lord of the Admiralty.
Continuing with the Lapwing in the Leeward Islands, Barton captured a number of privateers including the French Maria Topaze 10 off Montserrat on 28 December 1796, the Spanish San Christophe 18 to the north of Bermuda on 15 February 1797, the French schooner Le Heureuse Catherine 6, the Louis Bonsoi 4 on 9 June off Barbuda, and the Regulus 4 north of Tortola on 1 August.
Remaining in the Caribbean but exchanging with Captain Thomas Harvey into the French built twelve-pounder frigate Concorde 36 in the latter part of 1797, Barton continued his record of capturing enemy privateers by netting another dozen or more, including the schooner Caye du Pont 16 off St. Bartholomew on 3 January 1798, the schooner Proserpine 8 off Montserrat five days later, the Guadeloupe privateers Hardi 8 and Hazard 2 shortly afterwards, the Rosiere 2 off Montserrat on 1 April, and the Prudente 18 on 14 February 1799 off Antigua.
The Concorde returned to Portsmouth with a convoy from the Leeward Islands on 19 September 1799, having Vice-Admiral Henry Harvey aboard as a passenger, and after a period in dock she sailed from Portsmouth to patrol off Le Havre towards the end of January 1800. She re-entered Portsmouth on 6 March and sailed for Cork three weeks later, and she then appears to have taken a convoy out to North America towards the end of April. During this period it was reported that Barton broke some ribs when tumbling to the deck during a violent gale.
The Concorde served on the northwest Spanish coast during the latter part of 1800, and on 4 January 1801 Barton wrote to the Admiralty from Lisbon advising of his capture of the Spanish privateer lugger San Josef 6 off Oporto. His command was subsequently off Cape Finisterre on 27 January when she fell in with Rear-Admiral Honoré Ganteaume’s Brest fleet of seven sail of the line and two frigates. Disdaining flight, Barton drew the frigate Bravoure 40 some six miles away from her consorts and hove to, and although the action that followed did not result in a victory for either vessel, the Concorde enjoyed the better of it and would probably have taken her opponent but for the Frenchman’s approaching consorts. The Concorde lost four men killed and nineteen wounded during the action, the Bravoure ten killed and twenty-four wounded, and following the duel Barton took news of Ganteaume’s whereabouts to England, reaching Plymouth on 3 February and sending an officer by express to London.
On 8 April 1801 the Concorde went out of harbour at Plymouth and anchored in the Sound to put out on a cruise three days later, and towards the end of the month she was at Cork with the out-going Newfoundland convoy. In September, whilst still commanding the Concorde, Barton was appointed the lieutenant-governor of Newfoundland in the absence of any flag officer, but he soon managed to create discord with the experienced army commander, Brigadier-General John Skerritt, who could not tolerate his airs and graces. He returned to Portsmouth on 30 December with the Concorde after a twelve-day voyage from St. John’s, having made the fastest passage ever recalled at that time.
In early March 1802 it was reported that the Concorde was to be repaired and made ready for sea with immediate effect at Portsmouth, and in April she sailed for Torbay before returning to the Hampshire port on the 12th. In May it was announced that she had been paid off and recommissioned, by which time Barton had left her.
In August 1804, following a year commanding the Isle of Wight Sea Fencibles, Barton was appointed to the Raisonnable 64, which vessel came back to Portsmouth from the Texel on 27 November to be refitted after a gruelling seven months on the Dutch coast that had left her in a very poor condition. She then sailed for Cork on 29 December to join Admiral Lord Gardner’s squadron where she remained until she was detached on 4 April 1805 with several other sail of the line to join the Channel Fleet off Brest.
Removing to the Nile veteran Goliath 74 in May 1805, Barton sailed from Plymouth on 14 July with bullocks and vegetables for the Channel Fleet, was briefly sent to the Downs, and in early August was back at St. Helens prior to rejoining the Channel Fleet. His command enjoyed a profitable couple of days off Ferrol in August, taking the brig-corvette Faune 16 on the 15th after a short chase, and capturing the corvette Torche 18 a day later, recovering twenty-two and fifty men from each vessel respectively who had been taken prisoner when the British frigate Blanche 36 had been captured under the command of Captain Zachary Mudge by the French frigate Topaze 40 off Puerto Rico on 19 July. Further duty with the Channel Fleet followed, but by the time she came into Plymouth on 7 December, the Goliath was under the command of Captain Mathew Henry Scott.
Barton was next appointed to the newly launched York 74 at Deptford in August 1807, receiving orders in September to proceed from Woolwich to Sheerness. On 13 November she sailed from the latter port for Portsmouth where she joined the squadron under Rear-Admiral Sir Samuel Hood which captured the island of Madeira on 26 December. By February 1808 the York was at Barbados with a number of transports, and she spent the best part of the next eighteen months with Rear-Admiral Sir Alexander Cochrane’s squadron on the Leeward Islands station, being present at the capture of Martinique on 24 February 1809, in which campaign Barton commanded a division of seamen ashore, and later participating in the capture of the Hautpoult 74 on 17 April.
The York eventually returned home in the summer of 1809 with a convoy from the Leeward Islands to arrive in the Downs on 13 July. Two weeks later she departed that station with transports for the Walcheren campaign, and on 28 August she arrived at Plymouth with over six hundred French prisoners, having endured a long passage from Walcheren. She went out of the harbour on 5 November following a refit, and ten days later dropped down to Cawsand Bay to be paid, prior to sailing for the Mediterranean. During 1811 she continued on the latter station, participating in the fleet skirmishes between July and November. In February 1812 the York was sent home with convoys from Messina, Malta and Gibraltar numbering forty-three sail in total, but she parted company with her charges in the Straits to arrive alone at Plymouth on 3 April.
Barton left the York upon being promoted rear-admiral on 12 August 1812, and he did not see any further service. He was advanced to vice-admiral on 12 August 1819, and he died aged 79 on 16 December 1831 at his lodgings in Flora Place, Plymouth, a day after the death of his eldest daughter, Anna Maria, who had been attending him, and also the day after the death at Exeter of his son-in-law, Captain Francis Stanfell.
He married Anna Marie Downe of Northam, Devon, who died after a long illness in early 1828, aged 62. His eldest son, Robert Cutts Barton, entered the Navy but died as a commander aged 40 in 1827, and his second daughter married Captain Francis Stanfell in December 1810. His residence was given as Dix’s Field, Exeter and Burrough House in Devon. In November 1829 the death was reported of Charles Dunbar, ‘a man of colour’ aged 98 after 36 years service to Captain Barton.