
I fhis parents were not registered then ypou did not buy a puppy with papers. what you probably were given was a pedigree, even a mongrel can have a pedigree (list of ancestors) if details are known. A registered dog is different. You can only register a litter with the KC if the parents and their parents, grandparents and so on were also registered!
If the breeder of your dog bred both parents and their parents were registered it may just be possible to get them to register both parents and then register your dog. I beleive late registration carries a much higher fee, £50 for each late registration! I suggest you ask the breeder if they would be willing to do this, and contact the KC to see if this is possible.
Are you wanting to show the dog!