BA website
one standard-sized bag - maximum size of the bag must not exceed 56x45x25cm (22x17.5x9.85in) (including wheels, pockets and handles)
It is not a bag and they may object for that reason alone. Once they open the tubes, they may decide that they are dangerous weapons - hooks etc. Whilst they might think it improbable that you would assemble the rod and use it malevolently ... since it falls outside the norm, there must be a chance they will insist on it being checked as a special.
Just ask at the check in desk, don't wait until you get to security as that makes it more tedious to make your way back to check-in and a queue a second time. When you get back, you might drop by here to update the thread for future pax to search.