I'm pretty sure there's no such list, because it changes too fast. It's also a little dependent wether you count by zoos or by zoological organisations because both Antwerp and London run at least two zoos.
Moreover, do you count animals off exhibit or not and do you count fish and invertebrates? Solely on species, the names that are bound to appear in the top 5 in Europe are both the Berlin's, Moscow and Plzen Zoo (The last two hold and breed a large number of small animals behind the scenes).