Although nominally a 70 gun third rate of the 1745 Establishment, the Burford design was heavily amended by Joseph Allin, Surveyor of Navy, in 1754. She was ordered on 15 January 1754 as the first of five ships which made up the last group of 'traditional' 70 gun ships (they carried only 68 guns in practice) to be built before the 74 gun ship became the standard third rate. On 13 June 1754 she was named HMS Burford after her predecessors and the secondary title of George Beauclerk, 3rd Duke of St Albans and was the third and last ship of this name in the Royal Navy. She was begun by Master Shipwright Adam Hayes at Chatham Dockyard on 30 October 1754, then from August 1755 was finished by John Lock. Launched on 5 May 1757, she was completed on 15 July 1757. Her first commander was Captain James Young who commissioned her a month before launching in April 1757.^[2]

Burford took an active part in the Seven Years' War, initially with Admiral Hawke in 1757. In 1758 she was commanded by Captain James Gambier (who was her captain throughout the rest of the war) at the capture of Louisberg, then in the West Indies between November 1758 and November 1759. She rejoined Hawke on 13 November 1759 just in time for the Battle of Quiberon Bay on 20 November. She remained with Hawke until 1763, seeing action at Belle Isle in 1761 and the Basque Roads in 1762.^[2]

At the end of the Seven Years' War Burford was guard ship at Plymouth from May 1763 until 1770, with two expeditions to the West Indies as a troopship in 1764 and 1768. She was paid off in March 1770 for a Middling repair at Plymouth Dockyard (costing £11,317.6.2d) between November 1769 and February 1772, before going into Ordinary until 1776.^[2]

At the start of the American Revolutionary War Burford was commissioned under Captain G Bowyer for Ireland and completed fitting out at Plymouth Dockyard in May 1777. Between March and November 1777 she was at Portsmouth Dockyard fitting for the East Indies at a cost of £11,393.9.7d. Initially commissioned in May 1778 by Captain Taylor Penny, she was taken over by Captain Peter Rainier in October of that year before sailing on 7 March 1779 for service with Rear Admiral Edward Hughes on the East Indies Station. She participated in destruction of shipping at Mangalore on 8 December 1780, and then in the battles of Sadras, Providien, Negapatam, Trincomalee and Cuddalore against the French Chef d'escadre Suffren. In 1784 she returned to England with Sir Richard king, arriving at Woolwich Dockyard on 3 July 1784.^[2]

Burford was sold at Woolwich for break up for £1,320 on 31 March 1785.^[2]

The third Burford won seven battle honours: Louisburg 1758; Quiberon Bay 1759; Belle Isle 1761; Sadras 1782; Providien 1782; Negapatam 1782; and Trincomalee 1782.^[3]