You are discounting the fact that Britain endured the Blitz (September 7, 1940–May 11, 1941) well before Pearl Harbour (December 7, 1941). The Royal Air Force defeated the German Luftwaffe in the skies over Britain without US help. The Brits were helped by Commonwealth countries and pilots who had escaped from conquered countries in Europe. One of my uncles enlisted in the RAAF and was flying with RAF when his plane crashed in Nigeria, having been struck by lightning.
The British refused to surrender to the Nazis and suffered considerable privation by doing so. America only declared war after the Japanese attack and subsequent loss of the Philippines base. The Australian Prime Minister announced that Australia was at war immediately after Churchill did.
As for Vietnam, I don't recall that US was under any threat at that time. It was a foreign war that had a vacancy when the French withdrew. Once again, Australia joined in with the slogan "All the way with LBJ".
I think you should take a closer look at WW II history, in particular the dates. US did play a significant part in the victory but Britain joined the fight against Hitler from the time he invaded Poland in October 1939.