How do you you spell exercise in British English?

Normally, in British English, the consonant "s" is replaced by "z" , as in "recognized", organized, etc. Thus, should be, the answer to your question:

In "British English" it would be spelled: "exercized". Be carfeful of that, however; there is a move in Britrish English to emulate American spellings --- thus you well may find that (they) are spelled the same.