Of course Churchill had other options! The British could have signed an armistice in 1940 just like the French did. After the Great War, a lot of British people were opposed to the idea of getting involved in "another Continental war" and didn't want to provide the assurance to Poland that we would stand by them. For many business people in the UK (and the USA), the idea of going to war over Poland was "silly", they didn't see the Nazis as a risk to the British Empire, and saw Hitler as a bulwark against Communism. In the USA, many prominent politicians and business people did not want war between Germany and the British. People like Henry Ford had big business interests in Germany and were positively hostile to supporting the UK. Joseph Kennedy, the US Ambassador to the UK, was actively pursuing a policy of influencing Washington to refuse aid to the UK so Churchill would be forced to sign an armistice.
As for Hitler, he openly expressed his admiration for the "English Empire" and wanted to build an equivalent Aryan empire. He did not see Britain as a natural enemy of Germany. He did remember how the British had sent forces to Russia in 1919 to fight the Reds, and how Britain had overcome the impact of socialism agitators (unlike the French). Hitler was under the illusion that the British public were just looking for an excuse to ditch the French and join him in stamping out Communism. Some of that idea was due to British appeasers like Lord Halifax, some was due to British right-wingers like Mosely, and some was due to how the British had secretly supported Franco at the start of the Spanish Civil War. Once Hitler had convinced himself the British would seek a peace, he convinced himself there could be no other outcome. He was so surprised that he was rebuffed that he wasted weeks in June waiting for "the English to come to their senses". Even as late as July 11th 1940, Hitler and Admiral Raeder discussed invading Britain and Hitler described it as "the last resort", even though the Luftwaffe was then confidently predicting complete annihilation of the RAF in three weeks!
So, yes, Hitler wanted peace with the British in 1940. It's a historical fact.
Hitler had made clear his long-term goal was expansion into the East, so his clash with the Soviets was inevitable. Churchill had plenty of intelligence telling him Hitler wanted to attack Russia, and one of Churchill's aims was to try and bring Russia into the War against Germany, because he knew Hitler could not afford a two-front war. Hitler himself knew the Soviets were planning to attack, so he had to get a peace signed with or defeat Britain and get his forces to the East before Stalin was ready. Hitler had to leave the West in 1941 after failing to get that peace and after failing to defeat Britain in 1940.