Not sure the Glossy Ibis and two egret taxa entirely count for the purposes of the question, however, as all three are present due to natural expansion of their continental range as opposed to establishing from releases/escapes - though doubtless some given animals *are* from such origins.
Not forgetting the wild cats!!............. such as Puma etc...etc....... But maybe that is opening up a whole new can of worms which is best left closed ?
Wallabies on the Isle Of Man, I believe over 100. Pelicans in St James park London. Aesculapian snakes escaped from the Welsh Mountain Zoo and into the surrounding woods believed to number around 50.
An interesting thread. Regarding the Pelicans, although they are essentially "wild" in that they could roam if they wished to, to a degree, they do remain largely within that park area due to being regularly fed and they were introduced directly to that park, so that is a tricky one.
They have been seen in various places around the UK in recent years but usually only in small groups.
There used to be a colony of Mongolian Gerbils living on the Isle of Wight. However, the UK is too wet for them to become invasive. Same is true for prairie dogs. West Cumbria must be one of the wettest places in the UK. I can 't see them surviving there for long. However, prairie fdogs are notorious for escaping from captivity because they burrow so deeply. As for the parakeets. They are just everywhere in London.
There were albino wallabys in Milton Keynes a few years back, one got reported but locally a fair few people claimed to have seen them. Albino Wallaby
There are so many species that escape and breed for a few years but never really get established. In the 90's I remember reading about crested porcupine and giant squirrel in small populations. Terrapin species and snapping turtles have been found in almost every city lake. I have seen American mink, ring necked parakeet, wallaby, ferret, muntjac all within 20miles of my house. The occasional random pet escapes anything from inverts to large mammals!
There's a gang of about seven ring-necked parakeets who fly over London Zoo - in the autumn they landed in the trees of the squirrel monkey enclosure causing great interest, it was really surreal! The biggest groups are along the river in the east of the city I believe; flocks in their thousands roost there.
Also in the Poplar trees flanking Esher(?) Rugby Sports ground in the winter- unless they have moved elsewhere.
As well as all the more well-known exotics like grey squirrels, muntjac deer, parakeets and their ilk, there have been some very unusual species found in my home county of Essex: - In 1862, when red foxes were almost extinct in East Anglia and foxes from the continent were being imported, a golden jackal pup ended up in one of the shipments and was released into woodland near Ongar where it lived for several years - at the time it was referred to as a wolf. - In 1956, an Egyptian mongoose was killed near Greenstead Green and was initially reported as a pine marten (which themselves became extinct in the county over 100 years previously, in 1883). I do also know of a farm along the Essex coast somewhere with a sizeable feral breeding group of barnacle geese along with a couple of breeding pairs of red-breasted geese. There is also the interesting conundrum of some of the 'feral' herptiles that may not be feral at all - as well as the pool frogs which were once thought introduced but now considered natives, I have heard that the now-extinct New Forest colony of European tree frogs may have been native. Even read in some places that European pond turtles in the Broads may still contain some native animals although most there are almost certainly of introduced origin.
Oh and of course there are terrapins thriving in Hampstead Heath pond/s – I saw one once – they're pretty big! Don't know what variety though.