In British English, both organise and organize are correct. In American English, it has to be organize.
One of the English sources that recommends -ize in BE is the Oxford University Press. However, I wouldn’t call -ize Oxford spelling. I prefer to use it myself, but there are a number of verbs that still have to be spelt -ise, such as advertise and exercise. Here’s a list. So it’s actually easier to use -ise.
Reasons to use -ise might be: it’s easier (see above), the EU English Style Guide recommends it (why?!), and some clients, whether British or German, will insist on it as the only correct British form. They are wrong, but may not wish to admit this. Also, a client may have a house style, and the translator should then stick to that.
June 2010 PDF of the EU English Style Guide. A handbook for authors and translators in the European Commission (lots of interesting stuff on legal texts here too).
1.2 Words in -ise/-ize. Use -ise. Both spellings are correct in British English, but
the -ise form is now much more common in the media. Using the -ise spelling
does away with the need to list the most common cases where it must be used
anyway. (There are up to 40 exceptions to the -ize convention: the lists vary in
length, few claiming to be exhaustive.)
The spelling organisation should thus be used for all international
organisations, even if they more commonly use the -ize spelling, e.g.
International Labour Organisation (its website uses International Labour
Organization, while Americans will write International Labor Organization).
However, following the rule in 1.1 above, the spellings of bodies native to the
USA and other countries that use the –ize spelling may be retained.
I like the second paragraph, which I can’t remember seeing before. OHIM is a European organization but it spells itself Office for Harmonization in the Internal Market, which I’ve always appreciated.
What has brought this topic to the fore is the latest entry in the JIPLP weblog, American spellings — or English? in which Jeremy, of IPKAT, receives a curt reply from OUP. The entry shows the problems of dealing with people who are convinced that -ise is the only correct British form.
A commenter there refers to a Wikipedia entry on Oxford spelling.
In digital documents, Oxford spelling can be indicated with the language tag en-GB-oed.
The Wikipedia article also disagrees with the Commission Style Guide on International Labour Organization.
Another peculiarity of OUP is its support for the serial comma (bread, butter, and cheese). It’s worth knowing that -ise and the serial comma are often, outside OUP, regarded as incorrect in British English.