Britain had no option but to fight Germany to the bitter end after the fall of France. British policy since the days of Louis XIV had been to prevent a single entity from dominating all of Western Europe. As Britain was a small island nation, her population and industrial potential were severely limited. Should a nation conquer western Europe and unite it. It would be a matter of time before it amassed a fleet capable of defeating the Royal navy and invading Britain or blockading it to starvation. That's why Britain organized so many coalitions against Napoleon.

Technology made this threat even more pressing. With the advent of bombers and submarines, it was possible for a nation to starve Britain to death or bomb its economy to ruin with submarine raiding or aerial bombing. Britain in 1917 at one point came to the brink of collapse as it had just 6 weeks of food left due to unrestricted submarine warfare. The entry of the US saved it.

In 1940, there was the added threat of aerial bombing. The Luftwaffe did not transition to a strategic force and neglected to conduct a scientific-industrial analysis of the British economy. Had they focused on night raids against British ports and supplemented it with air attacks against British shipping, Britain might've collapsed before June 1941. The He 111 was capable of easily bombing all British ports in Southern England with the BF 109 providing escort.

He 111 could have also mounted unescorted night raids on Liverpool and Birmingham. The Ju-88 otoh was perfect for interdiction of British shipping. Goering and Hitler squandered their opportunity and let Britain evade certain defeat.

The British elite understood this reality. If they had sued for peace, it was inevitable that Germany would in the future far surpass it and be capable of easily defeating Britain. Germany in 1940 after regaining west Prussia, Austria, Sudetenland, Alsace Lorraine and Hostein had a German population of 83 million. In addition they also ruled over another 100 million NW euros and slavs and had access to all their mineral resources, industry and technical knowledge.

Britian had a measly population of 45 million and their little island had no other resource save for coal, tungsten and iron. She was not even capable of feeding herself. Against an entrenched empire of 180 million, she stood zero chance. She would've lost in 1940-41 had the Luftwaffe selected the right targets and strategy.

Thus, the British elite had two choices:

a) Become a vassal to Germany like Italy.

b)Continue the war and hope that the arrival of Russia and America would tip the scales.

They chose the latter but they ended up as vassals to the US. In retrospect, option a) looks superior but in 1940, option b) looked better. They couldn't know that it all end up in such a mess. Britain's own ineptitude led to the loss of South east Asia to Japan and Roosevelt's treachery led to Stalin taking over half of Europe. Thus at the end of the war, Britain was left with no choice but to submit to the rule of Washington and disband her empire.

It was all one tragic farce. It would've been best had the war never started. If Hitler had never invaded Poland. The assassination of Ferdinand in 1914 started the death slide of Western civilization, Hitler's invasion of Poland cemented it.