Not a capital city but what about the Bristol zoo ?
Haven't they managed alright in terms of finances, available space and with getting visitors whilst also managing the ex-situ conservation of the "little brown jobs" ?
They have, but they still have lions, fur seals, gorillas and pygmy hippos, which I suspect are more of an initial draw than tree kangaroos or palm civets.
They also (a lot like London) have ring tailed lemurs, squirrel monkeys, meerkats, and otters (+ red pandas), which are a subsidiary draw for average zoo visitors, I think.