Kirkley Hall's quite new, but I'm not sure. Anyway if this includes small zoos with the only animals being emu, goats, rabbits, meerkats etc. than there will have been a lot opened recently.
Wild Place opened in 2013, more recently than Kirkley Hall which opened in 2011. However I believe the former collection has held BIAZA membership from opening, whilst the latter only joined BIAZA in 2014.