OK lets assume for a moment that Force Z survives in relatively good shape and Malaya holds. How long before certain elements in the US start making noise about how the British are letting OUR BOYS STARVE in the Philippines and doing nothing to help them. Why is this powerful fleet sitting in Singapore drinking Gin Slings rather than RESCUE OUR BOYS? Why is Britain obviously prepared to FIGHT TO THE LAST AMERICAN to save THEIR COLONIES?
"Sorry chaps, we’re a bit busy stopping the Japanese right now, but rest assured we'll try to help when we have a free moment. Toodle pip."
You can't take Sumatra without taking Malaya and you could attack Java but it would be high risk and leave your supply lines exposed. Now this is the Japanese so they have form for "high risk attack with unsecured supply lines" but still.
Well they could try to go for Sumatra after (if) they take Java.
There's no good options. If these troops arrive, and considering the scale of the proposed reinforcements I think at last some are going to get diverted and Japanese get an accurate picture they are going to have to reconsider and at that point the choice is between bad (ignore Malaya) and worse (attack Malaya and get stomped).
Ignore Borneo and Java until Malaya is secure? That allows them to divert those troops.
The real question is if someone in Britain looks at how many good toops they have in the region and decides that they can protect more than just Malaya by for example dispatching a Division to Borneo or scattering some brigades across the DEI.
That's always a risk.
The Empire is going to struggle to keep Singapore supplied let alone Corrigedor. Singapore is an island and Siam is hostile. The Northern end of the Malay Peninsula is a war zone anyway.
It is important to remember that the RN expected even a fully developed Singapore to fall. It existed to provide a few months to get a fleet out East. Otherwise it is just another Malta scenario
If they don't take Malaya immediately, they'll have to surround it, by taking Java and then Sumatra, which won't be easy.
The issue with that is twofold. First of all the British Army is well aware that the SE Asia theatre will require a very different doctrine and equipment set to operations in Europe and therefore will want to be building up the British Army of Liberation in the European theatre with lots of tanks and heavy gear while separately having an Imperial force fighting a much more logistically and terrain constrained fight in the Far East. Secondly advancing through Thailand and Indochina is a very long way across very difficult terrain while attempting an island hoping campaign from South to North requires a Royal Navy commitment that simply isn't possible as long as the Germans have battleships lurking in Fjords and the Italians have ships in their northern ports.
Remember however that Britain doesn't only have territory in Malaya, but also Burma, which is much closer to the main part of Thailand. Also, a good portion of the RN contribution will be not from surface units, but the silent service.