Rilk A bird which flies upside down to prevent shit snow from going in his face (Porridge).
Ozzium bird:Flies round in ever decreasing circles and eventually disappears up its own arse. (Navy Lark).
Basket creature: Not much is known about these creatures, except they feature in Book of Revelations and live in laundry baskets. (Marty).
Norwegian Blue: Variety of parrot. Normal state: demised. Pines for fjords... (you know what...)
Giant hedgehog: Answers to the name of Spiny Norman. Usual cry "Dinsdale!"
(as above)
Siberian Hamster: A variety of hamster which looks like a rat. Found only in one pet shop in Torquay. (Again, you know what...)
Without resorting to sci-fi, fantasy or Flanimals, any more?