It's also worth pointing out that Singapore is overwhelmingly ethnically Chinese, while Malaysia is Malay. This seems to have preyed on peoples minds quite a bit. Add in a massive RN presence and Japan just over the horizon, and I can't see the UK letting Singapore go.
At the moment I'm assuming an earlier Indian independence (largely due to the war finishing earlier), but because Congress and Linlithgow kissed and made up in 1940 the Muslim League is much less powerful so it's heading for a loose federation rather than a two-state solution. This also helps with the Princely States who quite like their autonomy.
Regarding Singapore, that's true, though it seemed to have preyed on the minds of the British (who were concerned what the Malays might think about Singapore's large Chinese population) and on the minds of some Malays. It seemed to be less of a consideration for the Singaporeans themselves as both the first chief minister (David Marshall of the Labour Front, who was born to Sephardic Jewish parents that immigrated from Baghdad in the Ottoman Empire) and one of his opponents in Lee Kuan Yew of the PAP (who was ethnically Chinese) pushed for joining Malaya over 1955 to 1962.
Malaya's chief minister, Tunku, had initially rebuffed these attempts to court union over the racial issue, but gradually became concerned over the possibility of an independent Singapore becoming controlled by a hostile government or Indonesia eventually attempting to take it or influence, so by mid-1960 he had begun considering unification.
Of course one massive difference between OTL and TTL might be the effect of a lack (?) of a communist China and how that might have affected views on ethnic Chinese in Malaya, Singapore and Borneo. After all the Malayan Emergency was fought against the Malayan Communist Party's armed guerrilla force (MNLA/MPLA) and the leader of both the Party and its armed force was an ethnic Chinese Malayan and most of the support for the MNLA came from ethnic Chinese Malayans . A major strategy of the Emergency was to forcibly relocate around half a million (mainly Chinese) rural folk into the "New Villages" as a way to cut off the MNLA from its support base (and deport about 10,000 suspected Malayan/Malaysian Chinese communists back to the newly established People's Republic of China in 1949).
Without a Japanese invasion (?) to have weakened British imperial control over rural Malaya and to strengthen the Malayan communists (as they became allies of necessity for the British during OTL World War II) it is quite possible that we don't see Malayan communist guerrillas gaining the strength to cause major concern as in OTL and that subsequently, ethnic Chinese overall are viewed with less suspicion in the late 1940s into the late 1950s (that isn't to say that the Malayan leaders will want to embrace the ethnic Chinese, but that this might be one less reason to be hesitant over the Chinese as besides just upsetting the balance or dominating the federation, there would be less concerns over the ethnic Chinese acting as a fifth column and as a source of Communist Chinese influence in the region).
In this world, Japan might take the place of Konfrontasi era Indonesia as well as communist China of OTL in being seen as a the Big Threat in Asia. With Japan as the threat (and presumably Japan still having adventures in China), then if Singapore retains its importance as a RN base and the early decolonization of India leads a Dominion of a looser Federation of India (as somewhat envisioned in the 1935 Government of India Act) that retains stronger Commonwealth ties (reminiscent of how Australia, New Zealand, South Africa and Canada acted in the Commonwealth from 1920-1949) then there would be ample reason to maintain British forces in Singapore/the Far East.
Malayan chief minister Tunku might then be less concerned about Singapore falling under the control of an unfriendly government (since the British will remain) and so he might also be less inclined to consider unification (since he can get what he wants without accepting union with Singapore). He might however be open to continued integration in other forms (Singapore and Malaya already used the same currency by then anyway - the Malaya and North Borneo dollar), such as further civil service integration, education, aspects of trade and in defence.