Without Britain, WWII would have been lost with the invasion of Poland. The Russians only entered the war because Hitler's forces would be split. The US only entered the war because Japan attacked Pearl Harbour.
And without the Royal Navy and assorted British Imperial troops holding the line in Asia and the Pacific, the US would have struggled to reassert itself later in the Pacific. Yes, the British were pushed out of Burma and Malaya, but Japanese forces were kept out of Australia and India (iirc, they were held in Borneo).
We can say what we like now about appeasement, but we were in no position to go to war against Nazis. Even in 1939, there weren't enough British and French troops to hold back the invasion of France. After Dunkirk, Britain was wide open to invasion: while many troops were evacuated from the beaches of northern France, a huge amount of kit was lost. Invasion was expected, hence the training of the Home Guard and the development of the Auxiliary Units - groups of men whose job was to go to ground as a Nazi invasion swept past, and pop up behind it and start shooting up staff cars and blowing up railway lines and bridges. They expected to die, if push came to shove. The Battle of Britain was more the Battle FOR Britain: if Hitler had been able to take out the RAF, invasion would have been relatively easy. So yes, in that sense, Britain barely survived - but Britain was nonetheless key to the eventual Allied victory. The country put itself on a war footing, and turned the tables, slowly but surely.
And without war materiel from the US and the UK being shipped in via the Arctic convoys, the USSR would have been in a desperate situation. Arguably, without the notorious Russian winter and the willingness of Stalin and his generals to accept incredibly high casualties, Hitler would have taken Moscow.
World War II cost Britain a huge amount in blood and treasure, but it is not a 'false memory' to recall that the country and its empire were absolutely crucial to the defeat of the Nazis.
I would also take issue with the description in your later post of events in Gaza as a genocide, but that is another argument and not the topic of this thread.