Could history be different had the British attacked and taken over South Thailand in 1941 , thus prevanting the Japanese Invasion of Singapore?
Stop them - I don't think so. Hold up the Jap advance - yes, to some extent, until reinforcements could arrive. But what reinforcements, & how effective could they be? From top-down: Churchhill was juggling between various Empire needs worldwide; superior American intelligence didn't always inform Whitehall (& in any case misread Jap intentions); the Malayan Command & particularly air logistics were already overstretched; & the Commonwealth & Indian-Army troops deployed in were of various quality. Even Force Z was fatally complacent.
The British appreciated the strategic importance of the Kra Isthmus long before it became a "forward defence" plan under Ops Matador. They thought that it could be a staging area from which to bomb India, & also a canal possibly dug out (partly funded by Jap investments) to strangle S'pore's prosperity. But IMO to actually invade there, with or without Thai permission, would complicate matters a lot. Politically, attacking a neutral country would alienate the Americans. Territorially, the British wouldn't be after real estate as much as just securing airfields & potential beachfronts. (Un)Realistically, any such advance to set up defensive positions must be launched as soon as the Jap fleet set sail from Indo-China, except they lack adequate intelligence to time such plans without creating a possible embarassment instead.
Ultimately, Churchill called the shots &, whether well-advised or not, he gambled that S'pore could be defended by a local garrison & sea power. He's said to be very skeptical about the air-power factor, which Matador relied upon & which ultimately didn't matter cuz the British had problems protecting all the airfields in Malaya itself.
Instead, the British fled N. Malaya and allowed the N. Malayan states to be annexed by Thailand, only to demand the states (kelantan, perlis etc) back from the Thais after WW2.
Thailand never "annexed" Northern Malaya; it was the Jap conquerors who pulled the strings. The British "demanded" them back post-WWII only for their inclusion of the new Federation of Malaya, but IMO without any insidious motive since they already sensed that the old colonial relationship could no longer be recreated.
I get you're generally implying, however. Those states were "rootless" vassals until fairly recently, being Siamese protectorates until the mid-19th C & then incorporated as "Unfederated Malay States" within the British sphere of influence thereafter till WWII.
I also wonder if Malaysia currently has a plan similar to Ops Matador to prevant the Thais from staking their claims over N Malaysia?
Those states are firmly under Malaysian sovereignty since then, & Thailand respects that. Neither side envisions annexing each other's territories as "forward defence", if that's what you mean. Doubt the local Muslim population there would accept Buddhist-Bangkok jurisdication either, since they're intimate with how alienated their fellow faithfuls in southern Thailand already feel.
If anything, if you wanna define by old Siamese dominion boundaries, a bigger claim would be that Thailand owned Cambodia & Laos more (before losing both to the colonial French).