I think that we all understand that. However, as has recently been suggested, it sounds as if they are being 'unreasonable', such that you might be able to get somewhere if you were prepared to do enough fighting. As I said (and eric implied), you'll obviously get nowhere by continuing to argue with the BCO, who will presumably never change his/her position - so you would need to 'escalate' your complaint to 'above his/her head'.Just to bring it back to problem in hand …. They want certification of original electrician, or pay them to do it.
However, as I recently wrote, only you can decide whether you think that the time and hassle of fighting ("on principle"), rather than just paying LABC, makes sense for you.
Kind Regards, John