I know that in American English they use "-ize" instead of "-ise", in a lot of words like (recognize, legalize, criticize, etc.). But I'd like to know if in British English they use only "-ise" or both of them.
-ize or -ise
The Oxford English Dictionary prefers -ize, while I think Cambridge uses -ise. The second spelling is more popular in the UK today, but -ize is not unknown.
"-ize" was, traditionally, how it was spelled in British English, and as Josh said, the OED prefers this spelling. But in modern British usage, "-ise" is predominant.
I second what Lazar and Josh said. Both are used in British English, -ise being a bit more prevalent as it was taught in schools that way.