Britain never had any serious intent of fighting for Czechoslovakia, even if the Munich Conference hadn't happened, and Germany went to war with Czechoslovakia, Chamberlain deep down probably still would not have gone to war over the country. The British cabinet debated on how to respond to the German overtures towards Czechoslovakia, Germany wanted permission to attack the whole of Czechoslovakia, but Britain said that they would only support the annexing of the German populated, Sudetenland. So this is when the Munch Conference happened, as both sides felt if they could meet face to face (rather than through intermediaries and diplomats) that they convince the other to see it their way. On the issue of Czechoslovakia, the British foregin minister Sir Alexander Cadogan wrote in his diary:

Foreign Policy Committee unanimous that Czechoslovakia is not worth the bones of a single Grenadier. And they’re quite right too!”

So its important to establish that Chamberlain did not believe that Hitler would at all be satisfied by the Sudetenland, or even the whole of Czechoslovakia (which Hitler would take months after the Munich conference). As soon as Chamberlain returned home, he ordered all relevant industries to begin re-arming for war, France too sped up their re-armament, which had started in 1936. Neither nation's military was really ready for war, France was in a decent position being that they had started re-arming earlier, but they were still short of crucial armaments like artillery, tanks, anti-aircraft guns, and aircraft. Britain's military was an even in worse position, and to compound British military problems, many of the dominions, such as Canada and South Africa had made it clear that they weren't ready for a war, and would not be able to support Britain.

Now the British public as a whole was relieved, as no one really wanted, what in most people's minds, a repeat of World War One. However, the issue of appeasement and the way which Chamberlain went about it divided the British public. For Chamberlain's supporters appeasement was a time honoured British tradition of keeping peace on the European continent. Britain was used to this system of "give and take" as a means of keeping the peace. It also represented a way of bringing stability to Europe, which would allow Britain to focus on its Empire, which was in danger from an ever expanding Italy and Japan.

However, there were those who bitterly opposed the policy of appeasement. Churchill and his supporters denounced it as cowardly and weak. Churchill was a big fan of putting Germany back in its place. The left wing was offended by the abandonment of the principles set out by the League of Nations (such as self-determination). Far Leftists saw appeasement as a tool of capitalism, and they argued that countries like Ethiopia, the Spanish Republic, and Czechoslovakia, were being given up to fascist countries because fascism would eventually devour the USSR (the only real communist state at the time).

Chamberlain's fatal flaw was that he kept naively thinking that war could be postponed until Britain was absolutely ready. On March 15th, 1939 Hitler invaded the rump state of Czechoslovakia, and annexed the Czech parts, while setting up a Slovakian puppet state under a catholic priest named Joseph Tiso. Mussolini was not far behind and invaded Albania on April 7th. In the face of this aggression and violation of the Munich Treaty, Britain and France guaranteed that Poland would be protected from any German aggression. Chamberlain wasn't the biggest fan of this policy and kept thinking that there was a way to postpone war, even when it was clear that war was right around the corner.

Sources:

The Rise and Fall of the British Empire by Lawrence James

1938: Hitler's Gamble by Giles Macdongh

The British negotiated with Ireland to return the so called treaty ports and end the Anglo Irish economic war.

Part of the agreement was Irish neutrality . Reading accounts of the negotiations by participants they were surprised at the speed of the deal and were told war was on its way.

Ireland's neutrality was agreed then in 1938 to keep Ireland in Britains sphere of influence.

State papers are available here

Churchill opposed the return of the treaty ports to Ireland but was out of favour. The Irish had reason to fear a German backed civil war based on intelligence based on the Spanish Civil War.

I am sure that he believed war was inevitable.I am convinced that based on his policy towards Ireland but believe he thought he had time to spare . He hadn't set up agreement with Indian politicians and other commonwealth nations which he would have done if he thought war was imminent.