not sure how it works, although I did lose my reg certificate and was issued with another for £2 It's £5 now and they will only issue a duplicate registration certificate to the registered owner.
http://www.the-kennel-club.org.uk/asp/PEDI/A related point here, I know I've seen it mentioned (cannot remember if it was here or elsewhere) that PetLog will transfer ownership of microchips without having the current owner's signature. Again it's not quite as easy as that. I had one dog I'd bred back a few months ago. She was still KC registered in my name but her microchip was in the former owner's name. I could not (for various reasons) obtain a signature. I contacted PetLog and they sent me a special form to fill in, applying for transfer of ownership of the microchip without the previous owner's signature. For this I had to write down how I had got hold of the dog, why I had not got a signature, and I had to send as many supporting documents with the application as possible. (In my case I had emails from the former owner asking me to take the dog back.) PetLog then contacted the former owner and I assume it was either a case of being told yes, you can transfer, or not getting a reply at all and after x amount of time not waiting any longer -in any event it took many weeks before I finally had the transfer of the chip through, when it normally takes days. So it clearly isn't done lightly -even when the dog as in this case already was KC reg'd in MY name. (As that had never been transferred.)