Durrell together with the Zoological societies of London and Frankfurt are probably in a league of their own. But there are plenty of other zoos / zoological societies that have a (relatively) large involvement in conservation projects like Chester, Leipzig, Cologne, Zurich, Apenheul, Antwerp, Burgers' Zoo to name some.
The RZSS (Royal Zoological Society of Scotland) has a big involvement in various programs such as the reintroduction of European Beavers in Scotland. Shame that Edinburgh does not live up to the exception that London does. Although the Budongo does a good job.