Also would the US meddle with India, knowing how important it is for Britain ? Putting pressure on Britain "Don't forget to give independence to India as you promised" is one thing, but directly interfering while India is still British... Thing is, the US want to keep their friendship (or at the very least decent relations) with Britain.
As of now in the story? yes. But Indian independence is likely getting delayed again - there should be no arrest of the Indian National Congress, as by the time that should be arising as per OTL, the British will be in a much better position to handle it as per OTL. From there on, you could end up with the UK supporting the Muslim League (which isn't as strong as OTL as the aforementioned was not jailed) against the INC, and in total they end up continuing their divide and rule strategy either by supporting the minority against the Indian majority, or by supporting a larger Muslim Dominion within the larger Indian Raj, or straight out cutting their losses and supporting a greater Pakistan that would remain their ally.
Regardless, assuming the war ends ahead of schedule, with the UK and France and Japan being tied into a close alliance (the US isn't needed at the head of the alliance so much as there should be a strong Italy on the continent who is anti-Soviet. Whether or not Italy can make up for the US (they can't) they can make the appearance of the position of France et al being stronger, reducing the need for the strong alliance).
It's not going to be one big event. But combine a delayed and bloodier Indian independence on top of Suez being forced through by the Anglo-French (and ignoring censures by the US and USSR) combined with Algeria and combined with any number of other events we haven't considered in the postwar world (any China/Germany fallout, Indonesia, etc). Combine that with armed standoffs and blunders, and it could be forced in that direction, though the drifting would take years. This Cold War, as it were, may not even begin until the 60s officially, but could grow until then.