
it does depend on wether the pups was fit for sale at the time you bought it.
As a living being you are in effect buying a work in progress, not a finished item, so good bad or indifferent as the breeder may be, could they have been reasonably aware that there was a potential problem with the puppy.
If this abnormality was not something that could have been foreseen (as in a known genetic issue, or something either parent had, then really it is just very sad.
If this problem was present at the time of sale then you have a case with trading standards if the seller was in business. If a private seller, Then it's
'buyer Beware', it was up to you to ensure the puppy was fit at teem of purchase, just as with a purchase of a second hand car bought privately.
Check if there are other adverts for other litters (anyone breeding five or more litters in any 12 months requires a breeders license from their Local Authority, you can check with their LA to see if they are licensed).
As has been said the only official registry for dogs in the UK is the Kennel club, all others are simply used for dogs that can't be registered with the KC.
The reasons not to register with the Kennel club are never good, it means either the parents are not registered, or have restrictions (endorsements) placed by their breeder not to be bred from,(might be to ensure they are health tested first or they are unsuitable for breeding), the bitch was too young, too old, or had to many litters (Kennel club will register a maximum of 4 litters in a bitches lifetime).
These other registries are primarily used by commercial breeders/puppy farmers, and purely commercially motivated back yard breeders with unregisterable stock, to give them an air of meaningless respectability (makes them more sellable).
Anyone with a serious interest and knowledge of their breed will be breeding within the Kennel club and breed club umbrella, sharing knowledge and information with other breeders and owners, in order to produce the soundest puppies in a breed that has the potential for health issues directly related to it's conformational traits, if over exaggerated.