Woburn Safari Park, all the animals are in the open and you drive through for ages. Got lions, tigers, giraffes etc. Not that close to dorset but its close to the areas you’re talking about

There is the Hawk Conservancy near Andover. Well worth a visit.
Finkley Down Farm, also near Andover.
Finkley is aimed more at families but I just take the kids as an excuse to go myself. I love it there!
Butser Hill National Nature Reserve, part of Queen Elizabeth Country Park, if you like to look at beautiful views and hopefully some butterflies.
Here is a list of other wildlife centres in this area. Some I have visited but not all.

Monkey World
Wareham
Dorset

There is also a wildlife conservation park in Kent but I can’t think of the name – I’ll come back to you on that one.
Kent Wildlife Trust.