I didn't say that in BrE one has to use 'apologise'; I just said that the spelling occurs in BrE. American usage accepts only aplogize, while British usage accepts both. Consistency is key.
The following is taken from the Oxford Dictionary for Scientific Writers and Editors
-ize (or -ise)
In British English the -ize form of this suffix is now often the recommended ending for most verbs, with -ise as an accepted variant. It is important to chose a convention and stick to it, i.e. do not use more than one spelling of the same word in the same document.
However, note this:
-yse and -yze
The spelling -yse is preferred to -yze in British English as the suffix for verbs derived from lysis.
[...]
The preferred American spelling is -yze.
Therefore, I prefer to use -ise as well. If we strive for consistency, then this somehow feels wrong: "He apologized and then analysed the data."