Is there any software to regularize British vs. American spelling in a text?
Yes. There is an add-in for Microsoft Word called myWriterTools that will convert US to UK English and vice-versa. It also highlights changes so you can double-check. It isn't free however.

Alternatively you could use CTRL + A to select all your text in the existing document and set the proofing language to your desired version of English. This will then show the majority of errors as incorrect spelling (be wary of words such as license and licence though which may be used in different contexts) in Word.

Compass in a comment has mentioned an online converter US2UK that may be useful for shorter documents.

I have searched for a LaTeX equivalent but it would appear one does not exist currently.