Appeasement
Although Hitler offended the Treaty of Versailles in several ways, the Western powers - and especially Great Britain under the government of Neville Chamerlain - did not interfere for a long time. This kind of policy is called "appeasement". Great Britain was in a deep economic crisis at that time and therefore, they wanted to avoid another war. So, they made concessions to Hitler: they tolerated Hitler's invasion of the Rhineland, his nuclear armament and initiating the compulsory military service (which was all against the Treaty of Versailles). The annexation of Austria was not considered as problematic by Britain. They regarded it as an intestine matter of Germany and Austria and Hitler referred to the right of self-determination of the peoples. Britain even finally agreed to the annexation of Sudentenland. In the Munich Agreemnt of 1938 they (together with France) allowed Hitler to annex it and referred - as Hitler had done it before - to the self-determination of the peoples.
Great Britain agreed with Germany that the Treaty of Versailles was too strict and that its regulations prevented Germany from achieving economic and social progress. Thus, they were sypathetic about the German wish to revise the Treaty. Additionally, they believed Hitler, who assured them to lead a policy of peace. Great Britain assumed that Hitler would proceed much more aggressive if he planned to start a war. So, one can say that a problem of the British government was its underestimation of Hitler.
Britain only ended their policy of appeasement in 1939 when Hitler invaded Poland. Chamberlain was strongly criticised for his kind of policy.
Sources:
MacDonough, Frank. Neville Chamberlain, Appeasement and the British Road to War. Manchester: Manchester UP, 2000.
Parker, Robert Alexander Clarke. Chamberlain and Appeasement. British Policy and the Coming of the Second World War. Basingstoke: Macmillan, 1993.