A quick count on Zootierliste for Edinburgh gets up to the high 70's. Unfortunately I haven't got the time at the moment to scrutinise in detail and check for duplications or off-show animals but I would imagine it's a contender.
This is a fascinating thread, but hard work. I've just revisited the Edinburgh information on Zootierliste and can't come to a definitive number. Basically my memory (I only get to visit annually, most recently in September) is not up to the task. I don't make lists like some I know do and can't remember whether/where some of the more obscure (generally smaller) mammals were on-show (I'm fairly sure, but not certain, there wasn't Lynx or Beaver on display for instance).
Can anyone who visits regularly put a number on it?
Also, ZG can you clarify whether the Chester number includes domestics (I think it does) so everyone can compare like with like?