Prime Minister Chamberlain declared war on Germany because he had no other political choice at that moment. The Munich Conference in which he held much faith proved to be his greatest oversight. Between 1938 and 1939 Hitler's demands grew in hostility. Hitler understood Chamberlain's motives for signing the Munich Agreement, (to prevent further hostility and/or war) and used those very motives to further his own agenda. Hitler was a master of deception, he backed Chamberlain into political corners, first at the Munich conference and second with the declaration of war. Those two events unfolded exactly the way Hitler wanted them to. Unfortunately Chamberlain never saw it coming even as he was warned by another Englishman, Winston Churchill.
The primary reason for Chamberlain's declaration of war came in his realization of the failure of his politics of appeasement. Chamberlain believed that if Hitler's demands were met in terms of land acquisition as well as little interference from the West. The notion of appeasing Hitler in his demands to avoid war became known as appeasement. Chamberlain was motivated to pursue this policy because the horrors of the First World War represented an end whose avoidance was something that was at the forefront of Chamberlain's mind. In believing that war could be avoided in the hopes of "peace in our time," Hitler and Chamberlain signed many agreements that were to be honored, the most pressing of these was the accord which stated that Poland would not be invaded. Too much of a gentleman to realize that Hitler wasn't, Chamberlain was genuinely horrified when Hitler and the Nazis invaded Poland in 1939. His declaration of war was the affirmation of the failure of appeasement, and the realization that in doing everything possible to avoid war, Chamberlain and his policies might have actually caused it.
Many historians think Chamberlain's 'appeasment' was simply buying time for rearmament. Towards the end of the war Hitler often had tantrums about being 'tricked' by Chamberlain into delaying the start of major conflict. By the time Hitler invaded Poland (seventy years ago today), Britain had beefed up it's military hardware and had made many military preparations.
Obviously, Chamberlain hoped Hitler wouldn't grab anymore of his nieghbours' land, but he didn't just sit there with his fingers crossed! He switched the country towards a 'total war' footing and got ready. History has remembered him unkindly.
Chamberlain finally declared war because Hitler launched a naval attack against the strategically vital port of Gdansk in Poland and had mobilised a massive invasion force which swept across western Poland. Hitler's previous land-grabs had been low-key, localised events. But the invasion of Poland was a massive and irreconcilable move. It was a clear statement of intent to dominate the whole of Europe.