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.
Nouns
compromise
demise
disguise
enterprise
exercise
franchise
merchandise
surprise
Verbs
advertise
advise
apprise
arise
chastise
circumcise
comprise
compromise
demise
despise
devise
disguise
enfranchise
enterprise
excise
exercise
improvise
incise
merchandise
premise
prise
revise
supervise
surmise
surprise
televise