As Sooty said, there have been no Walsrodes or even Avifaunas in the UK. Two of the best have survived at Birdworld and Birdland, although perhaps shadows of their former selves? - but there were some of the others which stood well above the rest, Olney and Kelling springing to mind. Some of the others were important but scruffy, like Stagsden and Rode. Many of the others were pretty poor to dreadful even for their day, though some were nice like Midland, Padstow and Ventnor. Many were private collections which had overgrown themselves, but many a zoo goes back to these same origins! Blackbrook of course is an exception, as it is much more recent.
At the time there was a culture of bird-keeping. From post-war years working-class people people bred pigeons, and budgies, canaries and poultry, plus 'foreign' birds. This was fed by the huge commercial bird trade. Also returnees from the remnants of Empire brought back a culture of shooting and an interest in pheasants and waterfowl both of which were very popular with breeders. 'Animal people' from this era onwards were (and are!) the famous names like Lilford, Bedford, Ezra and Delacour, Grahame, Wayre, Scott, Sims...
Bird Gardens/Parks were cheap to set up as public expectations were pretty low, there was a ready market for the progeny if you were good at it, and a ready supply of imported new stock if you weren't.
Those days have largely gone, the birds replaced by reptiles which are the modern fashion..