As far as I can see from his Service Record, he served on
Oct 1939 June 1940 DRAKE 2 Barracks at Devonport
June 40 Feb 42 MAORI Destroyer
Note: various parent establishments noted during this time, they would have been responsible for admin / pay etc:
TYNE depot ship
DRAKE Devonport barracks
NILE base at Alexandria, Egypt
Feb 42 Jan 43 HERO Destroyer
Jan 43 Dec 43 WOOLWICH Depot Ship; then based in Egypt
Dec 43 Fen 44 NILE
Feb 44 Jan 45 DRAKE
Jan 45 - Sep 46 MAYINA Camp at Colombo, Ceylon [Sri Lanka]
Sep 46 (1 day) LANKA Base at Colombo
Sep 46 Mar 47 DRAKE
Mar 47 Apr 47 VICTORY Barracks at Portsmouth
Apr 47 Oct 47 DRAKE
Oct 47 Feb 48 IMPERIEUSE Training establishment at Devonport, which consisted of
several ships, RENOWN, VALIANT and UNICORN
Feb 48 Jun 48 DRAKE
Jun 48 Jul 48 RENOWN Battlecruiser; static training ship at this time
Parent establishment for admin was
UNICORN aircraft repair ship
Jul 48 Jan 49 DRAKE
Jan 49 Jul 49 CAMPERDOWN Destroyer
Parent establishments for admin and pay were:
UNICORN
HOWE battleship
Jul 49 Sep 49 DRAKE
Sep 49 Apr 52 GRAVELINES Destroyer
Parent establishments for admin and pay were:
DRAKE
ST ANGELO Base at Malta
PHOENICIA Base at Malta
Apr 52 Jul 52 DRAKE
Jul 52 Aug 52 CALEDONIA Training establishment Rosyth
Aug 52 - Jul 54 DRAKE
Jul 54 Nov 54 PRESIDENT HQ and Reserve units London
Nov 54 Nov 56 CUMBERLAND Cruiser
Nov 56 May 57 OCEAN Aircraft carrier
May 57 Oct 59 HOGUE Destroyer
Oct 59 Jan 60 VERNON Base Portsmouth
Jan 60 Mar 61 MURRAY Frigate
Mar 61 Oct 61 DRAKE
You mention other ships - Cleopatra - Sphinx - Rockwood - Emperor - Atheiing - but they do not show on his record - I would think that this is because he would have been 'loaned' to those ships, while remaining on the books of his parent establishment