Is it correct to write -ise instead of -ize in Britsh English?

Both -ize and -ise are used by British people. Neither is correct, or incorrect. You'll have some people say that one spelling
is American and the other is British, but not true. The choise of -ize and -ise sometimes depends on the etymology – words with Greek routes are -ize where as Latin routes are  -ise. The Oxford English Dictionary standardised on -ize thus this spelling is sometimes referred to as "Oxford spelling". Both the King James Bible and Shakespeare used -ize endings throughout. The Times newspaper prefers -ise at all times except for in the word capsize. Both Britain and American people mix them up. For example, Americans will write advertise with an -ise ending. Choose whichever spelling you like and stick with it. What is wrong is to sometime use one spelling and sometimes use another.