Chestnut Centre, however, isn't in the area in question
Despite the "mixed" reputation of the collection on this forum, if you have not visited South Lakes in the past I suggest you probably should, if only to make your own mind up about the collection.
Unlike the Northwest, which is relatively well-stocked with zoological collections, the Northeast of England is pretty starved of collections

but there are still a few collections you should look into visiting:
Kirkley Hall Zoo - a small zoo, affiliated with a local college and used by students on Animal Management courses and so forth. It is open to the public on weekends and - outside of term time - weekdays, and has rather a lot of nice little treasures, including a wide selection of unusual reptiles and amphibians, pure Rufous Lemur, New Guinea Ground Cuscus and a decent collection of cranes and ibises.
International Centre for Birds of Prey (Duncombe Park) - a sister site to the long-standing collection falling under the same umbrella at Newent in Gloucestershire. Despite having been open for little more than two years, it is already the best falconry centre in the north-east as far as I am concerned, and contains a wide range of unusual taxa such as New Zealand Falcon, Booted Eagle, Lesser Kestrel and Verreaux's Eagle.
Yorkshire Wildlife Park - a large collection growing by leaps and bounds, filling a niche which has not been filled in the area for a long time. Highlights of the collection include the only polar bear exhibit in England. However, unlike the previous two collections mentioned it has been much discussed on Zoochat so I can probably leave the description at that.