The only way for Britain to have not entered the war would have been for BOTH France and England to acquiesce to the invasion of Poland. It would appear that they hoped against hope that by signaling that both France and Britain would support Poland (following Germany's conquest of Czechoslovakia the preceding March and in full knowledge that they would never be able to physically support Poland) that Hitler would stop and back away from a general war. But as others in this thread have suggested, the West had had enough. Chamberlin would have been replaced quickly if he had not finally taken a stand.

After his long string of successes in brinksmanship, Hitler simply didn't think the West would have the nerve to stop him. When his hoped for successes in Denmark, Norway, and eventually France materialized, he really did view it as a possibility that England would sue for peace rather than fight an unwinnable war against Germany. Historians suggest that the British would likely have received generous terms as well -- at the price of ceding Europe entirely to the Nazis and Fascists. And there were English pols who advocated just such a course, believing that it would have preserved the Empire (which was doomed long since by the sweep of history, WW2 at best hastened it a bit).