How did the Japanese conquer Malaya in just 55 days?

This episode examines the Centers of Gravity for both the Allies and the Japanese during the Malaya-Singapore Campaign.
A centre of gravity is a key characteristic, capability or locality from which a force, nation or alliance derives its freedom of action, strength or will to fight. It can also be described as the primary entity that possesses the inherent capability to achieve an objective or the power to exert influence.

British Centre of Gravity: The Singapore Naval Base at Sembawang
The British operational planning was dominated by the requirement to protect the Singapore Naval Base at Sembawang. This was incorrect and fundamentally flawed. It was assumed that the powerful Royal Navy fleet would deter or defeat any aggressor in the Far East. However, the base was never big enough to host the planned deterrent fleet. Budget and treaty constraints, including the Washington Naval Treaty, as well as later WWII commitments, meant the fleet never arrived.
The British Far East Command attempted to compensate with air power, but British forces had to hold terrain deep in Malaya to prevent Japanese airfields from being used to bomb Singapore. This forced static defence rather than trading space for time. RAF Far East was drastically under-equipped (e.g. Vickers Wildebeest still in use). No tanks were deployed to Malaya, and intelligence failed to account for Japanese tanks.
Japanese Centre of Gravity: Offensive use of the Tank
The Japanese centre of gravity lay in their ability to sustain aggressive, mobile operations—especially through the innovative and effective use of tanks.

Tanks as COG: Type 97 Chi-Ha and Type 95 Ha-Go tanks used as infantry support in “filleting attacks.” This worked very well against the British, who had no tanks and little in the way of anti-tank weapons. Surprise and psychological shock played heavily in the campaign. Soldiers trained in the jungle, with combat experience and aggressive infantry tactics that had been refined in China and Manchuria, overwhelmed the Allies who struggled to coordinate between units and to generate the combined arms effect.

Britain tried to preserve a naval base they couldn't use whilst Japan leveraged an aggressive offence that overwhelmed an unprepared enemy operationally, tactically and temporally.
As Sun Tzu said, strategy without tactics is the long road to victory, but tactics without strategy is the din before defeat. Here we see the Japanese with both the strategy and the tactics. The result was the fall of all of Malaya in just 55 days, and Singapore, the Gibraltar of the East, would fall just 15 days later.