Although Russia has had its imperial moments in history, Britain has always wanted to be the world's little bully landlord. With it's impressive Navy it pulled it off all over the world, particularly with small island territories line itself, and primitive countries that they could swiftly overrun with their military might. However, with Eastern Europe being mostly unapproachable by water, this was not such easy meat. They needed a place where they could set up camp, a home away from home. They utterly dominated India, yet India was more than 10x the area of Britain and certainly more than that in population.
Part of Hitler wanting to take Poland first was so he could use it as a vantage point to eventually attack Russia. I think it's likely that Britain with its imperial tendencies also wanted Poland for similar reasons, to give them a vantage point to eventually fight with Russia. And in turn Russia wanted to control Poland because it is basically the Eastern gateway to mainland Europe. But when the Germans got control of it first, and also attacked Britain, Britain was forced to ally with Russia because of the simple "enemy of my enemy is my friend" rule. However, Britain's real attitude toward Russia was revealed immediately after the war. And they did everything to get America and eventually Israel to help control and contain the East Bloc. I believe that Britain has had a vendetta against Russia as a rival empire and threat to its own expansion for long time. I also believe that British Intelligence has created many false flag scenarios in the world to demonize Russia with the U.S., Israeli and other allies using allied global media.
So, basically I think Britain would fight over Poland simply to keep the door open for its own expansion with Russia as it's main concern. And Hitler became their main competitor over the same goal.