[2] Falmouth was laid down on 23 November 1957 by Swan Hunter & Wigham Richardson, launched on 15 December 1959 and was completed on 25 July 1961.

[4] On 5 December that year, Falmouth collided with the oiler RFA Tideflow in Lyme Bay and was badly damaged.

[4][10][11] On the evening of 6 May 1976, after the outcome of the Third Cod War had already been decided, the Icelandic gunboat V/s Týr was trying to cut the nets of the fishing trawler Carlisle, when Captain Gerald Plumer of Falmouth ordered it rammed.

[12] Falmouth also sustained serious structural damage on her bow during the incident,[13] and had to enter dry dock at Portsmouth for repairs.

[14] In January 1977, when the United Kingdom enlarged its Exclusive economic zone to 200 nautical miles (370 km), Falmouth was deployed in the North Sea, protecting fishing stocks and oil fields.

[15] Falmouth left active service in 1980, when she was transferred to the Standby Squadron at Chatham, and by early 1982 she was being considered for disposal as a result of the 1981 Defence White Paper, which proposed cuts in the Royal Navy's surface fleet.

[4] Falmouth was laid up as a stationary training ship at HMS Sultan in December that year, and was scrapped in Spain from 4 May 1989.