The British new their existance as a people was not at stake, only a position of Empirial priviledge that was disappearing anyway. So they were more reluctant to take casualties for places like Singapore. Had their Island being invaded, perhaps they would not have been so shy fighters during the war.
For the other countries you mention I am dubious about the somewhat glib summation of their outlook you give, but this particular one does not accord with my appreciation of the situation at all.
In the first place, the British people were quite clear that their whole way of life was what was at stake; Nazism was quite clearly incompatible with their hard-won traditions of democracy and gradually developing tolerance. The chances of the British government, especially with Churchill in charge, agreeing to a detente with Nazi Germany was nil.
In the second place the Imperial position was by no means "disappearing" before the war at all - it had never been stronger, in fact. Its nature and constitution was changing, but then it had done so since before it was even regarded as an "Empire", so that is hardly surprising. It was in the later stages of the war and thereafter that the "Empire was lost", as some would have it. The reasons were mainly US influence, the fact that Britain was economically drained by the war and the nationalist movements that were in many cases deliberately encouraged as a force on one side or another in the war itself.
Finally, the loss of Malaya/Singapore had nothing to do with 'shy' fighting - the troops defending there were mostly Indian, not British, and though they did not lack either skill or determination there were too few of them and with too poor a strategic plan. The root of the problem lay, in fact, in the strategic planning outlook of the Imperial government in the inter-war years, which was driven by harsh realities of what the Empire could afford. The strategy was one of "two out of three"; in other words, the Empire had to operate in three theatres - the Home Islands, Northern Europe and the Atlantic was one, the Mediterranean and "Middle East" was a second and India and the "Far East" a third. The Imperial forces were constituted to be able to deal with serious threats in any two of those theatres at one time. When serious threats arose in all three at once (from Germany in Northern Europe and the Atlantic, from Italy in the Mediterranean and North Africa and from Japan in the Far East) the Imperial Government found itself catastrophically under-resourced, with no coherent plan and pretty close to out-and-out panic. The command paralysis, insufficient defence force and general mishandling of the situation that led to the fall of Singapore was the most obvious result. The bottom line is that the British Empire at the end of 1941 had one full-size army and two full-size fleets to cover three large arenas of operation - it wasn't enough.
I would say more about the multi-ethnic nature of the USSR and how it was far from clear that their "extermination as a people" was at stake, but rather they were motivated (as many times before in history) by a basic love of Mother Russia or their respective homelands, a dedication to Communist ideals (albeit possibly brought about by brainwashing - but what belief in a political system is not, to some extent?) and fear of the 'Political Officers' - but my knowledge in that area is less well founded, so I'll leave it to others.
