The Soviet Union was an ally of Nazi Germany in 1940. It was not until 22 June 1941 that Hitler invaded Stalin's Soviet Union (with which he had had an alliance until then, and which had co-invaded Poland with him and divided it up between them) and brought the Soviet Union into the war against him). Nazi Germany had invaded Denmark on 9 April 1940, and the country fell in days. Nazi Germany invaded Norway on 9 April 1940, and the country was conquered by 10 June. Nazi Germany invaded the Netherlands on 10 May 1940. The Dutch forces surrendered on 15 May. They also invaded Belgium on 10 May 1940, and the Belgians surrendered on 28 May. They also invaded Luxembourg on 10 May, and that country surrendered one day later. The Nazis also invaded France on 10 May 1940, and France surrendered on 25 June. The Nazis invaded Greece on 6 April 1941 (though the Italians had invaded on 28 October 1940) and Greece fell (except for Crete, which fell on 1 June 1941) on 23 April 1941. Poland, of course, was invaded by the Nazis on 1 September 1939 (and by the USSR on 17 September 1939) and fell on 6 October 1939, with Germany and the USSR dividing up the country.
Canada, Australia, India, etc. were part of the British Empire, so, of course were counted on the British side.
Britain and its Empire stood alone against Nazi Germany, with no other allies (except Greece for part of the time) for a year, from June 1940 to June 1941 (when Hitler stupidly invaded the USSR).
Sure, a few refugees from conquered countries fled to Britain to fight on. But presumably they might have fled to Bombadil's realm in Middle-earth to do the same.
Sure, Britain eventually gained other unexpected allies. The USSR, because Hitler stupidly attacked them. The USA, because Japan stupidly attacked them, and then Hitler stupidly declared war on the USA in support of his Axis ally.
However, the moral of this story is certainly; There is a point in resistance to evil, even if it seems hopeless, or at least desperate. "Oft evil will shall evil mar!" Allies can spring up from unexpected places! Refugees from defeated realms can bolster your own strength!
Who's to say that refugees from Rivendell, the Havens, and Gondor wouldn't have made their way to Bombadil's realm to aid in the fight? Who's to say that Sauron would not have made stupid mistakes that brought say the Easterlings or the Southrons (or both) into the war against him?
I just am certain that the concept that there was no point in resistance, just because all else had been conquered, would have probably been totally alien to JRRT, living when he did and where he did, and, most importantly, believing what he did.