South Lakeland Zoo has been having lots of trouble recently. Animal welfare issues have been but one of the causes for concern. We went last year and it was somewhat tatty. Parrot house was good, but you will have to work to get good shots elsewhere. The council have recently refused to renew the operators licence for the owner guy so a new set up is in place, but I think they are being watched very closely. Not a place We'll be rushing back to.
Leighton Moss is well worth a visit. You can easily spend all day wandering between the hides. Lower hide regularly sees otters, kingfishers, bitterns and marsh harriers; providing you are patient. You are a birder so will have the patience that I lack!
You might be lucky and see red deer from the Tim Jackson/Grizedale hides, but if you want deer then a trip to the opposite end of The Lakes, to Martindale will give you deer. You can drive all the way up the valley and there is a shooting lodge (The Bungalow on OS maps) but you might still have to walk up the hillside.
Depending on when you go the ospreys might still be at Foulshaw Moss. You go right past that on the road to Ulverston. Ospreys also at Bassenthwaite near Keswick. I'm also told that there are ospreys on Esthwaite Water this year and you can hire a boat to go out on the lake to see them. The publicity is that they will dive into the water right next to your boat: we all believe that don't we? If you are inerested....
http://ospreysafari.com/osprey-safari/
Depends how far you want to travel. Caerlaverock(WWT) in southern Scotland is well worth a visit, but may be too far for you.
Walney Island off Barrow has colonies of seals and seabirds.