Why didn't Britain and France do anything about the remilitarisation of the Rhineland?

Chamberlain was acting on the policy of appeasement, so he was trying to meet Hitler's demands in order to avoid another war. Hitler was planning to pull out of the Rhineland as soon as Britain and France told him to, but they never did. They were fearful he ould declare war and reject the Treaty of Versailles, so hey said he was 'marching in his own back yard'. However this made Hitler more confident that he could get away with break more terms of the treaty, especially having seen the effects of the Manchurian crisis, so he was only stopped when he eventually invaded Poland in 1939. (Also Britain and France were a bit tied up with the worrying situation with Mussolini in Africa, and basically the League of Nations was falling apart so there was nothing much they could do anyway.)