Only two scenarios I can see for Britain not declaring war:
1-Germany doesn't move into Czechoslovakia in March 1939. This was the moment Nazi Germany openly moved from 'reuniting German peoples' to straight out conquest. Without this they might have had the leeway to move against Poland under the pretext of protecting German citizens.
2-The Poles do something remarkably stupid like launching a pogrom against the Germans in Danzig or threatening East Prussia and thus set themselves up as the aggressor.
1-Germany doesn't move into Czechoslovakia in March 1939. This was the moment Nazi Germany openly moved from 'reuniting German peoples' to straight out conquest. Without this they might have had the leeway to move against Poland under the pretext of protecting German citizens.
2-The Poles do something remarkably stupid like launching a pogrom against the Germans in Danzig or threatening East Prussia and thus set themselves up as the aggressor.