Dudley Woodcock was born in Portsmouth, Hampshire on 6 December 1909, the son of Abel Thomas and Emma Annie Woodcock (née Watson). He joined the Royal Navy as an Engine Room Artificer Apprentice on 3 August 1925, and, on completion of his five-year apprenticeship, he served in the battleship HMS EMPEROR OF INDIA. This was followed by the cruiser HMS CHAMPION, the battle cruiser HMS HOOD and the destroyers HMS ANTELOPE, HMS SALADIN, and HMS GRENVILLE. Engine Room Artificer Third Class Dudley Woodcock was promoted to Warrant Engineer on 1 January 1938 and, after post promotion courses he was appointed to the aircraft carrier HMS EAGLE on 1 March 1938.

He was appointed to the Submarine Depot Ship HMS FORTH ‘for Submarines‘ on 18 February 1941. This was followed by an appointment to the Submarine Depot Ship HMS MEDWAY at Alexandria on 15 July 1941 and to HMS THUNDERBOLT as the Engineer on 11 February 1942. THUNDERBOLT (previously HMS THETIS) was lost with all hands in the Mediterranean off Cap San Vito, Sicily on 14 March 1943.  THUNDERBOLT was detected, in the early hours of 14 March by the Italian Destroyer CICOGNA. Following a three-and-a-half-hour pursuit, CICOGNA made a depth charge attack at 0845. This brought the stern of THUNDERBOLT to the surface before the submarine finally sank.

Dudley Woodcock was the husband of Morwen Mai Woodcock (née Jenkins), and is commemorated on the Portsmouth Naval Memorial on Panel No. 73 Column No. 1.