Hi,
I'm guessing DEFRA would be about the only place that might be able to answer fully - iirc any list such as you are seeking would be spread out over a couple of different acts such as the DWA and the invasive species act.
I'm also not sure if you would want to include CITES 1 in the list as, unless you are a zoo or research establishment, they really might as well be considered banned as well in practical terms. Ditto for any animals that do not live long enough to get through quarantine (small list though I would think).
It's a lot simpler to ask them about a specific species really.
dr del