"Havock" was engaged on escort duties for the next six months, including escorting the carrier during the Battle of Taranto on the night of 11/12 November, aside from a refit in Malta from 22 December to 20 February 1941. During the Battle of Cape Matapan, she torpedoed and sank the on 28 March. The ship evacuated Commonwealth troops from Greece at the end of April and was one of three destroyers escorting the light cruiser when they bombarded Benghazi on the night of 7/8 May. "Havock" was damaged by dive bombers on 23 May, killing 15 and wounding 10 men, after a patrol off Heraklion, Crete. She was under repair at Alexandria until 16 June. The ship bombarded Vichy French positions in Lebanon in early July and then began escorting ships to Tobruk until October when her propeller shafts and propellers were damaged. "Havock" was under repair from 21 October to 4 December at Alexandria.