In the early days, the only aviary was a small macaw aviary next to the honey badgers at howletts housing scarlett and blue and gold macaws. Later, they just held a pair of blue and golds and these bred in the 1st primate cage past the African Elephants, before disappearing from the collection.
Howletts used to have a pair of adujant stork where the lion-tailed macaque compound is now....in a grassy enclosure in front of one of the tapir paddocks. They also had free-roaming guinea, jungle and peafowl.
Port Lympne held double-wattled cassowary and emu when they first opened. The emu were near the top of the park and the cassowary were in the wood lower down, where most of the primates are now held. They also had some pheasants and quail briefly where the current amur tiger house is. Most interesting were the pair of black-necked storks, which were kept in what is now the bush dog enclosure. They were amazing birds, and I have never seen one since.
I don't think any of the storks or ratites bred. I would imagine there are at least some birds now....