Bristol Zoo, Wild Place, Bristol Aquarium (and Noah's Ark if you fancy it) are all within the Greater Bristol area.
Newquay Zoo, Newquay Blue Reef and Paradise Park in Hayle are within 20 minutes of each other.
Cotswold WP, Croc's Of The World and Birdland are also within 20 minutes or so of each other.
Living Coasts, Paignton and Shaldon Wildlife Trust are in 3 adjacent towns on the South Coast of Devon, again all within 20 minutes of each other.
That's all the UK ones I can think of right now. Probably think of some more tomorrow.