Among the general public appeasement was considered a dividing topic but the slant was definitely towards appeasement, the majority of the media, and public opinion polls showed the British public favored appeasement. There are several theories for why appeasement was popular but the generally accepted one is that much of the British public had gone through WW1 just 20 years ago and had been bombarded with messages about how WW1 would be the war to end all wars, so the public was naturally against any action that might spark a new war.

Now politically it was in no way unanimous and Chamberlain's appeasement was highly divisive. Generally the right wing was supportive of appeasement as it prevented a war without weakening Britain, the left on the other hand, hated appeasement because it went against the principles of the League of Nations. The Left Wing branded Chamberlain the "Arch-appeaser" and some even went as far as calling him a "proto-fascist".

All the criticism Chamberlain gets for being weak and naive is really unfair to Chamberlain in my opinion, Chamberlain wanted to isolate Hitler, while Britain rearmed. He knew Hitler wouldn't stop with the Sudetenland, he just wanted to buy time to get his country into a position where could it threat Hitler militarily and diplomatically isolate Hitler by repairing relations with Mussolini.

Source:

The Rise and Fall of the British Empire by Lawrence James

This paper gives a pretty good overview as well. http://www.loyno.edu/~history/journal/1993-4/Lilly.html