In 1938 Britain had signed a Treaty with Germany where Germany promised to undertake no further conquests. The conquests so far had anyway been mostly territories that had been part of Germany itself until 1918, and the union with Austria had broad support in Austria - Austria had even asked for that union as far back as 1919, only to be refused by the Allies.
Britain was moreover woefully unprepared for war in 1938 and its Government knew its forces and equipment (apart from the Navy) to be inferior to that of Germany. Moreover, France at the time would absolutely not do anything to antagonize Germany and the US was firmly isolationist. As a consequence Britain would be utterly alone to fight Germany's superior army. So in a way it was solid good sense at the time to appease Germany, rather than to fight it.
In 1939, Britain and France had together guaranteed Poland's independence, so Britain now knew it had an ally which it considered (wrongly, as it was to turn out) a strong military force. Britain even then was more or less forced into war by Germany's invasion of Poland. For almost a year afterwards Britain nor France gave any follow-up to their declaration of war, only to be forced into action by Hitler's invasion of France a year later.