Prescott was commissioned lieutenant on 22 May 1758 and promoted commander on 28 November 1777.
He was posted captain on 8 April 1778 and commanded the Queen 90 with the flag of Vice-Admiral Sir Robert Harland at the Battle of Ushant on 27 July 1778. After leaving the Queen towards the end of the year he joined the Seaford 20, taking a convoy out to Quebec and returning to serve with Commodore Charles Fielding?s squadron which detained the Dutch convoy in the Channel on 31 December 1779. He then commissioned the new Mercury 28, going out to Newfoundland in April 1780 and serving briefly with Commodore George Johnstone?s squadron off Lisbon from the end of February 1781 before returning to Newfoundland for the 1781 season. He recaptured the cutter Sprightly on 17 May and eventually left the Mercury in 1782, whereupon he did not see any further service.
In 1785 Prescott became infamous after being tried for ?wanton, tyrannical, unprovoked, and savage cruelty? to his wife. The court heard disturbing evidence from many witnesses of his verbal abuse, deprivation of food, threat of firearm use and punching, kicking, dragging down stairs, burning with tongs, and caning. This despicable behaviour had began within a week of their wedding and continued through his wife? pregnancies, aboard ship and until she fled for her safety in November 1782. The verdict allowed Mrs Prescott a divorce through reasons of his cruelty, with alimony of ninety pounds per year.
Prescott was promoted rear-admiral on 1 June 1795, vice-admiral on 14 February 1799 and admiral on 9 November 1805. He died at the age of ninety-three on 3 May 1830, being at that time the second most senior officer in the Navy.
On 5 January 1779 he married Jane Walter. Her father, the Rev Richard Walter, was chaplain of Portsmouth dockyard and had been Commodore George Anson?s chaplain during his famous voyage to the Southern Ocean. Prior to her flight from Prescott?s brutality they had issue two sons, Admiral Sir Henry Prescott, and another son who drowned whilst returning from East India Company service in 1806.He also had an illegitimate daughter, Georgiana, born in about 1768.