Well, assuming it is like you say it is, you went to a TRANSFER DESK, rather than a check-in desk, where they apparently offered, I assume, to send someone to the baggage reclaim to find your bags, and re-tag them for LHR.

First of al, I'm amazed you ever saw any of the bags again.

But putting that aside, presumably by accepting their offer to do so, you were accepting BA's baggage policy. Which is clearly stated on the ticket, and the Manage My Booking.

The fact that they couldn't re-claim your bag doesn't surprise me, if they'd already sent someone to find the bags, re-tag them, and take them off to be loaded onto the BA plane.