Given you have suggested you want to visit small zoo's with birds and small animals, I too would recommend Lakeland Wildlife Oasis.
One of the few zoo's at present you will see a Fossa, they are also the only collection to houe Garter Snakes as far as I know.
Added to that they have Rodrigues Fruit Bats, Long Nosed Potoroos, Spiny Mice, Tenrecs (which are actually viewable and not in pitch black like Chester), Tree Shrews, Red Squirrel's, Brown Lemurs, and Snow Leopards.
Regarding birds, they house, Turacos, Java Sparrows, Bluepie and Crested Wood Partridge, of which all bar the Bluepie are free roaming so you can get up close.
They are also about to add Parma Wallabies and they also have a slow worm.
They are building a no roof Red Squirrel exhibit as well, giving the Red Squirrel's natural exhibits.
Whilst it may only take you an hour or two to have a thorough look round and take loads of photos if that's your bag, they certainly have a lot of nice exhibits for a small zoo and the staff are most friendly and helpful.
If you're up north it's definitely worth a visit.
If birds and small animals are also your thing I would recommend Beale Park which is between Newbury and Reading. They have a very large collection of birds and birds of prey and they have a number of small mammal species. They also have one of the best Lemur exhibits I've seen, which whilst it isn't a walkthrough, is absolutely massive.
Park map will give you more idea's.
Park Map - Beale Park
Again it's small and it's closed until February 8th, but if birds and small animals and good well made exhibits are your thing, it's worth a couple of hours to visit.