Most academic and technical writing in the UK still uses the z form, and the OED and Collins dictionaries tend to prefer it, too: https://en.wikipedia.org/wiki/Oxford_spelling
In popular writing, the s forms dominate - I've not heard the MS Word explanation before, but the most popular UK-produced word processors and spellcheckers in the 1980s (eg. Locoscript/Locospell, Protext/Prospell, 1st Word) tended to come from companies in the Cambridge area or which were founded by Cambridge grads, so would naturally have used the s spellings by default.
I'm British, but when submitting papers for blind review, always use American spelling for obvious reasons. I suppose I could change it after acceptance, but that would just be pretentious.
> Most academic and technical writing in the UK still uses the z form
'z' forms are generally used for writing for an international audience, it hasn't really caught on more generally than that.