Here's a link for you:
Toxoplasmosis in cats and man
Basically even an infected cat is rarely capable of infecting other animals, and then only through poo over a day old. It's pretty easy to see ways of making sure cat poo over a day old is not present in cages of suseptible animals.
In Australia, where there's wildlife that's vulnerable outside the cages, I guess it's reasonable to have a no cats policy (though I'd be glad to see animals which are possibly lost through no fault of the owner given a chance of re-finding them rather than being shot straight away... so glad to hear a recent comment!) But I don't think it's too difficult for zoos in other countries to have cats around without endangering their stock. Even in Australia I guess there might be times when a healthy and well supervised cat might be an asset?
London Zoo has at least one cat: I've met him. He's called Heathclift and can sometimes be found greeting visitors along the road on the way to the main entrance (though he ducks behind the railings when school groups come past). He apparently lives in keepers housing, I don't know if he spends much time in the actual zoo, but certainly could if he wanted to.