In March 1938, when the British made their decision (which they kept secret from the French), that Czechoslovakia was inherently unstable and unworthy of support it was really the end of the story. Nothing what happened later could have changed the outcome. Britain was the prime mover - weakened by the Great Depression, and the disastrous Popular Front's rule France was only capable of following Britain and basically nothing more.Between March and September 1938, the British government sought, with rising anxiety, to avoid the perceived danger of becoming engulfed in a disastrous war with Germany, precipitated by Czechoslovakia's German minority problem. In order to achieve that aim, it resorted to increasingly radical means of attempting to defuse the situation in Central Europe — culminating in the Munich Agreement. [...]
Britain's attitude was founded on the belief that Czechoslovakia was indefensible against a German attack; that due to its heterogeneous ethnic composition it was inherently unstable and unworthy of support; and that it was not necessarily inimical to British interests to allow Germany to extend its influence further into Central Europe. There can be no question of the British government not being conscious of the real relationship between the SdP and Nazi Germany. British policy-makers repeatedly indicated their awareness that Henlein was being controlled from Berlin, whilst simultaneously clutching optimistically to the contrary belief in the SdP leader's moderation and freedom from Hitler's influence. Equally, there can be no doubt concerning the British government's understanding of Germany's intentions towards Czechoslovakia. Hitler's stated objective of bringing all Germans into the Reich was accepted in Whitehall at its face value, and it was realised that the Sudeten Germans were included in that aim. The disruption of Czechoslovakia was an inevitable consequence, but that was considered not necessarily detrimental to Britain, particularly if it helped to secure the desired understanding between Britain and Germany, and only caused alarm because it involved the danger of armed conflict. The main imperative was to avoid war - not to limit German expansion in Central Europe.
The Runciman Mission to Czechoslovakia, 1938: Prelude to Munich by Paul Vyšný
The Polish leaders assumed that Britain was the key as early as 1936 (maybe earlier), and they knew Britain was disinterested in Central Europe - these two facts guided Polish foreign policy for the few next years.