I'm afraid that in British English the rule *is* different. We do indeed tend to use hyphens after the prefix "non-" (which avoids the possibility of mispronouncing words such as "nonnative" ["non-native" in BrE]).
As regards other prefixes, "pre-" and "co-" still sometimes take a hyphen (particularly where the second part of the word starts with a vowel and could lead to an erroneous pronunciation, e.g. pre-empt, co-opted). According to the Oxford English Dictionary, "micro-organism" is also the preferred form, for similar reasons.