"Glowworm" was ordered from the yards of John I. Thornycroft and Company, at Woolston, Hampshire on 5 March 1934 under the 1933 Construction Programme. She was laid down on 15 August 1934 and launched on 22 July 1935. She was completed on 22 January 1936 at a total cost of £248,785, excluding government-furnished equipment like the armament. Upon commissioning she was assigned to the 1st Destroyer Flotilla of the Mediterranean Fleet. "Glowworm" patrolled Spanish waters during the Spanish Civil War enforcing the edicts of the Non-Intervention Committee until she had a refit at Portsmouth between 27 May and 8 June 1937. The ship returned to the 1st Destroyer Flotilla in the Mediterranean after her brief refit. "Glowworm" returned to Portsmouth for a longer overhaul between 7 June and 25 July 1938 and escorted the ocean liner SS "Strathnaver" between Malta and Alexandria during the Munich Crisis in September 1938. She then escorted the light cruiser on her voyage to Aden later that month. During night exercises on 16 May 1939, "Glowworm" collided with her sister, , and was forced to put into Alexandria for temporary repairs. She received permanent repairs in Malta between 23 May and 24 June.