BA would have informed you of your rights to claim compensation during the booking process if you used their website or app. And the catch all is that there is usually a printed notice informing you of your rights by at least one of the check in desks which you are at liberty to read.

I doubt that online and printed notices are in the spirit of the intent of the regulation, but I have yet to find an airline that makes a very public announcement that compensation is claimable. I am sure there are a few examples out there when proactive announcements regarding compensation rights have been made, but I suggest it is rare.