The Centre of Gravity is that characteristic, capability or locality from which a force, nation or alliance derives its freedom of action, strength or will to fight. 

For the British, the CoG was the Singapore Naval Base.  It was the fundamental part of the defence of the whole of South East Asia.  In times of need the Royal Navy would sail out to Singapore and defeat all comers and ensure that the Empire was secure.  The port at Singapore was central to the defence of Australia.  The base wasn't big enough for the fleet required to keep the seas free.  The fleet was unlikely to sally forth if decisively engaged in Europe, so the fleet base was too small for a fleet that was unlikely ever sail there.  It turned out to be the second largest graving dock in the world at the time.

We look at how the Singapore Strategy became increasingly untenable, but no one was prepared to

In 1940 it became apparent that the Navy would not be able to sail to Singapore 'for the foreseeable future."

LT GEN Percival conducted an analysis of the defence of Singapore before the war.  This dictated that the defence of Singapore would need to be conducted in Malaya and northern Malaya at that.

As the war progressed, Churchill hoped that the US would provide the Navy required to support the British in the Far East, if provoked.

With no Navy to defend the base, the defence of Malaya fell to the Air Force.  With not enough planes and the planes they had being too old, the last line of defence would be the Army.

The defence of the base dictated the way that the Battle of Malaya was fought.

For the Japanese, the CoG analysis is a lot easier.  It was the tank.

The tanks the Japanese had were not great and the tactics they used were not modern, but they had tanks, used them very aggressively and the British had no tanks in Malaya.  The Japanese used the tanks for filleting attacks which were devastating, especially against forces that were not well versed in combined arms, or even anti tank weapons.

A Critical Vulnerability of tanks, of course, is the logistics tail required.  How will Yamashita overcome this?