Many people in the UK think that because the Americans spell most -ise/-ize words with -ize, that -ise must be the correct way to spell. In fact, just this once, the Yanks are more right in many cases.
For a verb or noun with "is" in its original stem word, use the -ise ending (e.g. vis (seeing) gives "televise"). Always use -ise where the verb and noun are the same (e.g. "surprise" (although the first edition of Robinson Crusoe allegedly uses "surpriz'd"...)). Anything that doesn't sound like "-eyes" uses -ise, such as "promise". A list of all (?) of these words is shown below. Everything else should take "-ize".
Always use -yse, not -yze. "Analyze" is not UK English.