George Greenway was born in Brecon in South Wales on 1 November 1909, the eldest son of Lieutenant Thomas Cattell and Mrs Henrietta Eliza Greenway (née Jackson). He joined the Royal Navy as a Cadet at the Royal Naval College, Dartmouth in May 1923 and passed out on 1 January 1927. He was appointed to HMS EMPEROR of INDIA on 15 January 1927 and promoted to Midshipman on 1 September 1927. On 19 April 1929 he was appointed to the HMS SUSSEX and promoted to Sub Lieutenant on 1 July 1930.

Greenway was appointed to HMS DOLPHIN for the Submarine Course on 4 May 1931, was promoted to Lieutenant on 1 August 1931 and, on 17 August 1931 appointed to HMS RAINBOW as the Third Hand. This was followed by HMS L56 as Third Hand on 21 March 1933, HMS STARFISH as First Lieutenant on 7 November 1934, HMS ROVER as First Lieutenant in the Fourth Submarine Flotilla on the China Station from November 1935 and HMS OSIRIS as First Lieutenant from May 1937.

After returning to UK, he successfully completed his Commanding Officers Qualifying Course from January 1938 and was then appointed to HMS H49 in Command. He was promoted to Lieutenant Commander on 1 August 1939. appointed to the Submarine Depot Ship HMS MEDWAY for Submarines. He was appointed to HMS ROVER in Command on 19 March 1941. HMS ROVER was sent to Suda Bay on the island of Crete to provide electrical supplies to the cruiser HMS YORK which had been badly damaged in action. Whilst alongside HMS YORK the submarine was also damaged by bombing near misses which resulted in smashed batteries and a leaking hull.

George Greenway left HMS ROVER and joined HMS TETRARCH in Command in July 1941. He successfully completed three Mediterranean War patrols. Leaving Malta for a fourth War Patrol on 26 October 1941 he reported his position to HMS P34 on 27 October 1941, after which HMS TETRARCH did not arrive in Gibraltar and was never heard from again. Although Italian Aircraft reported sighting oil slicks in the approximate area there is no way of knowing if they were anything to do with HMS TETRARCH and it was assumed that the submarine was lost with all hands (presumed lost on Italian mines off Cape Granditola, Sicily).

George Greenway is commemorated on the Portsmouth Naval War Memorial on Panel No 45 Column No 1.