other then a) doing what it did in OTL & losing it's Empire, much of it's power and getting bankrupted in the short term or
b) ending up as a Nazi puppet state like Vichy France?
Could it have done anything else? (such as staying neutral until Hitler declared war on the USA in 1941 & the USA was ready to fight in Europe.)
A. Hitler wouldn't have declared war on the USA in 1941, Pearl Harbor or not, if Britain had already dropped out the war.
1. One of the reasons why the Japanese felt able to attack in 1941, was the European war. In retrospect, we know now the much of British Empire, Dutch and Free French forces in the Far East were defeated by the Japanese, and if anything were overestimated by the Japanese - but we don't know that in retrospect, and we don't how the Japanese would have felt if these forces had been able to draw on Royal Navy and European reinforcements.
2. The main reason that German-US relations were bad, were German u-boats were sinking ships bound for Britain, and the USN had also started engaging German subs in an undeclared war.
B. Churchill made a number of mistakes during the war, but his handling of the summer crisis of 1940 led to the correct decision, to fight on
Churchill wanted to fight on, even if it meant defeat - and while he hoped for victory, in mid 1940, he expected defeat (he said himself he expected to be dead in a couple of months) .
In summer 1940, everybody, including Hitler, Churchill, and most of the world's politic and military elites expected Britain to be defeated, and soon. They nearly all, vastly overestimated Germany's capacity to bomb, blockade (via u-boat) and invade Britain into submission.
But in cabinet, Churchill couldn't argue that he was arguing to a fight on towards defeat, so basically he argued that even if a peace deal might have to eventually be reached, hanging on would at least get Britain better terms than a deal in summer 1940. I think this was correct argument (a peace deal say in Jan 1941, would have been much more favorite to the UK than one in say July 1940) - even if it was slightly disingenious of Churchill to argue it the time, when he really wanted to fight on to victory or defeat.