
Your only option is with the kennel club, there needs to be a document signed by those who own a dog to be transfered.
If it was done on-line I expect as in litter registrations, it says something like you must keep the signed transfer form in case of any dispute.
if you can prove you did not sign or give permission for a transfer to sole ownership the KC may well change it.
it won't help you with access to the dog though, that's a civil matter, and the owners as others have told you is likely to be considered the person who has care of the dog regardless of any documentation.
When I split from my first husband he abducted my dog, which had always been in my name, unfortunately he could not be done for theft as it was considered communal property.
Anyway to be honest what would be the point, if you really only want to have contact with the dog, over time you will have to allow bridges to mend with your friendship in order to have any hope of this, so taking any action would be counterproductive.