LOL - the AKC is not relevant in the UK
In the UK, the registry body is The Kennel Club, and registrations are done by breeders, not by purchasers.
Your puppy should have been registered by her breeder. And what you'd receive from the KC is a 3 generation pedigree showing her parents, grandparents, etc This would be the certificate you have? If you want an enhanced version (5 generation), you can purchase it from The Kennel Club on their website at
http://www.the-kennel-club.org.uk/ (click on the dog registrations icon at the top of the page, then choose pedigrees from the menu on the left).