As far as animal and bird species are concerned, the following are all regarded as 'naturalised' within the UK (although some are the object of eradication programmes):
Mink
Grey squirrel
Night heron
Ruddy duck
Canada Goose
Wood duck (Carolina duck)
Bobwhite quail
Source - 'The Naturalised Animals of the British Isles', Christopher Lever, 1979, Paladin (publ.)
Of course that's now a pretty old book.
Additionally, 'Fauna Britannica', Duff Hart-Davis, 2002, Ted Smart (publ.) lists Muskrat, Elk and Lynx (although the latter via 'circumstantial evidence' - there are many ongoing sightings of various 'big cats' around the UK but few - if any? - have been caught that weren't recent releases).
Additionally, re-introduction programmes for both Beaver (European, not American) and Wolf are currently being debated.
Hope that helps
Bob :-D