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?

-Does the "Ponytail-Rat" in OFAH count??

-From the Chevy Chase movie "Fletch Lives": The mysterious termite that multyplies by masturbation. http://www.anyclip.com/movies/fletch-lives/bug-buster/#!quotes/

i have heard rumors from mountain bikers of the :

Suicidal spoke squirrel : has a tendancy to try and find a gap between the spokes of speeding mountain bikes , usually with disasterous results for both the squrrel and mtb'er !

and also the famous ' purple headed trouser snake ' ....... say no more...

The dreadful spindly killer fish in "Potato"/Blackadder II

More human like 'new species':

Baldrick Considered a new type of life. The Baldrick in series 4 had apparently a mother in London zoo.

Deadly Sins: Demonic like creations representing the seven vices. Lust has the first name Lilian (and looks like Raquel Walsh...) (Original Bedazzled).

Episode of Open All Hours mentioned a frat, a cross between a ferret and a rat.

Making up comedy animals seems to be a rather dated phenomenon, you can't imagine Shameless or The Office doing it.

But there was:

Cardboard box: A dog substitute, walked using a lead.Daisy called her box "Colin" (Spaced).

The German comedy duo "Erkan & Stefan" (basically the German version of Ali G.) invented the so called "Dönertier". They argued that the meat in the doner kebap comes from a special kind of animal, the Dönertier (doner animal):

Plausible!