Welcome to FT, Hornem.

It's an unfortunate situation, but there's not much we can do because, on the salient matter of timing, your version of the story is different from BA's and we can't say which one is correct. When you checked in is not relevant, what is relevant is the requirement to be at the gate at least 20 minutes before departure time, when BA is scheduled to close the door and flight. If you are confident of your side of the story you should file a denied boarding claim under EC261 rules, but proof of this will be difficult.

Incidentally, there is a BA desk at HEL. It is located just to the right of the entrance, admittedly a little hidden from view. It would be to your back (and visible) as you queue for security screening.