Pigott was commissioned lieutenant on 28 March 1771, and after being promoted commander on 25 August 1773 he joined the sloop Swallow and served in the East Indies for the next three years.
He was posted captain on 22 February 1776 in order to sail the leaky Dolphin 20 back from Bombay, and he brought with him the sickly Midshipman Horatio Nelson who later ascribed his survival to Pigott’s care. After reaching Spithead in August Pigott paid the Dolphin off in September at Woolwich.
In the late summer of 1778 he recommissioned the Jason 32, taking a convoy out to Canada in the following spring. During 1780 he served with the Channel fleet, and he captured the privateers Le Duc de Mortemaint on 10 December and l’Industrie two weeks later. He subsequently fought under the controversial Commodore George Johnstone at the Battle of Porto Praya on 16 April 1781 and returned home from St. Helena with Captain James Hawker a passenger. Thereafter he saw service in North American waters where he captured the privateer Jolly Tar on 28 September 1782, and the Scammell, in company with the Renown 50, Captain John Henry, on 8 December. The Jason was eventually paid off in August 1783 after returning home.
Remaining unemployed throughout the peace, Pigott commissioned the new Tremendous 74 in the spring of 1793, serving in Channel fleet operations from October-December and at the Battle of the Glorious First of June in 1794, where he lost three men killed and eight wounded. Prior to the action the Tremendous was fouled by the Alfred 74, Captain John Bazely, and she lost her starboard stern gallery and cathead. Both captains blamed the other for the accident. During the battle he incurred the wrath of Rear-Admiral Thomas Pasley who could not understand why the apparently undamaged Tremendous raised a signal of inability, and he was one of the captains who failed to get a mention as having distinguished themselves in the action.
Pigott was raised to flag rank on 4 July 1794, and without seeing any further employment he was promoted vice-admiral on 1 June 1795 and admiral on 9 November 1805. He died on 2 September 1822 and was buried at Church of St. Mary the Virgin, Beddington, Surrey.
On 1 March 1791 he married Sarah, the eldest daughter of Captain Charles Proby. His residence at time of death was given as Beddington, Surrey.