I think the UK being willing to go to war over Poland
Well, only the UK didn't go to war over Poland, it never had any plan to liberate Poland at all, this was the real reason why the UK went to war:
ia803008.us.archive.org/13/items/leesearnoldthejewishwarofsurvival1947/leese%2C%20arnold%20-%20the%20jewish%20war%20of%20survival%20%281947%29.pdf
Chapter I of this book is about Poland.
en.wikipedia.org/wiki/Arnold_Leese
This is a written account by a Arnold Leese a true British patriot who among the "official" lies and deceptions tried to reveal the truth to the British people.
He was unlawfully imprisoned and held without charge for the duration of WWII along with many other British patriots under the undemocratic and dictatorial regulation 18B.
en.wikipedia.org/wiki/Defence_Regulation_18B