It appears that a Royal Naval Party is often a shore based establishment or an amphibious establishment, so the questions "which ship he served on" may be moot.
NAVAL PARTIES of the ROYAL NAVY, 1942-1991 shows the places where RNP 2420 served (some of them pretty land-locked like Delhi) but including a couple of periods on H.M.S. Bulolo:
2420: Flag Officer Force W & Staff (attached to Admiralty 10.44 – 11.44/left UK for Delhi 20.11.44/to Chittagong area 12.44/ to Burma (Akyab) 02.45/ Force W to Delhi 05.45/ in India to 08.45/embarked BULOLO) Chittagong 01.45/Akyab 02-03.45/Kyaukpyu, Ramree Is 04-05.45/Delhi 06-07.45/Bombay08-09.45/BULOLO 09-10.45/ Singapore 11.45 – 01.46/ title lapsed 02.46
The Imperial War Museum has material from January 1946 which refers to "Force W, part of the amphibious force that landed troops in Malaya" and this site mentions at least one office "serving in South-East Asia, on the planning staff for operations in the Arakan and Malaya, the so-called Force W" between January and December 1945.
War diaries such as the one here can give you some idea of what Force W as involved in.
And Wikipedia mentions HMS Bulolo:
Following another refit, the Bulolo was sent in 1945 to be the Headquarters Ship and flagship of Rear Admiral Benjamin Martin for 'Force W' off Malaya commanding the Allies retaking of South East Asia from Japanese forces. In September 1945, Bulolo was used to accept the Japanese surrender at Singapore.
The original ships logs for Bulolo for her time in the Far East are held at The National Archives