Greenwich was ordered from Moody Janvrin on 3 October 1745, and was laid down at his yard at Lepe on the Beaulieu River in Hampshire in November that year.

[4] Roddam cruised for a while off Cape Cabron, San Domingo, but on 18 March 1757 mysterious sails were sighted, which were at first assumed to be a small fleet of merchant ships being conveyed by two frigates.

Realising that with the wind in the Frenchman's favour, he could not escape, Roddam attempted to lure the frigate towards him, hoping to capture her before the rest of the fleet could intervene, and then send her immediately to Rear-Admiral George Townshend, the commander at Jamaica, with news of the French movements.

[6] The frigate soon determined that Greenwich was a two-decked warship, and sailed back to the protection of the squadron, which then came up and attacked, with action commencing at 9 a.m. when Diadème opened fire.

[6] Roddam assembled his men in an attempt to board the 64-gun Éveillé, but several of her consorts bore up and opened fire, damaging Greenwich's rigging and leaving her unmanageable.

After consulting with his officers, Roddam expressed his desire to fight on, but eventually agreed to surrender Greenwich, as further resistance would only cause further casualties among his men.

[10] Despite being outnumbered and outgunned, the British engaged the French squadron at 3.20 pm, with the fighting lasting for the next two and a half hours, until Kersaint signalled one of his frigates to tow his damaged flagship, Intrépide, out of the line.

[10] In doing so the French line fell into confusion, with Intrépide, Superbe and Greenwich falling aboard each other, and were heavily cannonaded by Augusta and Edinburgh until they were able to untangle themselves.

[11] After repairing some of the battle damage Kersaint sailed for France with the convoy, but became caught in a storm in January 1758 as he neared the French coast.