We're clearly talking about different things here.
In terms of small scale animal interaction, Chessington has more than most zoos. I thought people knew this. I've seen them walk the reindeer out on park, bring out skunks, binturongs, coati, rats, parrots and meerkats, they have the monkey walkthrough and the lorikeets and the petting zoo. Where at London zoo can you touch anything? A bird landed on me once there and I was told to "stop encouraging" it to do so.
I thought we were talking about stuff like hand feeding giraffes... Animal interaction has to be very controlled for H&S reasons.
Chessington definitely has higher attendance than any zoo...