The dearth of high quality bird collections (there is nothing in the UK on the scale of Avifauna, never mind Walsrode) and the lack of a truly first rate aquarium spring to mind immediately. And whilst opinions differ on the revamp of the Clore at London, forty years ago it was one of the planet's greatest collections of small mammals, which is not the case any longer.
And herpetariums - there are close to none in the UK, with the closest thing being Crocodiles of the World, but I'm pretty sure I've heard of zoos in Germany, Denmark etc that have full-scale zoos dedicated to reptiles/amphibians/inverts and fish.