"Churchill wanted to [...] ensure fair and free government in Eastern Europe, especially Poland, for whom in 1939 Britain had gone to war."
Poland was left largely without help during WW2.
If Britain and France would agree for a preemptive strike against Hitler the whole ordeal could be avoided in the first place.
If the help would come in the 3 first months of the war, most of the destruction could be averted.
Lets not forget about Warsaw uprising in which 11 old kids were fighting waiting for some sort of help to come from "allies". Percentage of the destruction was bigger than in Nagasaki, yet no brit around.