I am also based in London. When I work for American companies I attempt to use American spellings in code and documentation, because consistency matters. For general communication I use British English because I won't get American English right, humans and search mechanisms can cope with the difference and I can express myself most effectively that way.

Incidentally, isn't "based out of" mostly an American idiom? I usually use "based on" or "based in" and find "based out of" and "based off" conjure images of poorly constructed buildings. (Don't get me started on "based off of".)

I'm in the same situation. I use American spellings for code comments, documentation and internal documents, but British spelling for chat and email.

I write color when I'm talking to my American colleagues and colour when I'm talking to my Canadian ones lol.

If you are multi-national, use where you are based in i.e. London.

If you're Canadian, working in Canada, just use Canadian English. The Americans probably won't even notice, and if the Brits complain, then just point out that you're using the proper English for the country you're in now.

This assumes your company doesn't have an official policy on the matter.