For what it's worth, here is another foreigner's opinion who has visited British zoos the last two years. I have only been to three, so my experience is limited: Port Lympne Wild Animal Park, London Zoo, Chester Zoo.
As others have said, Chester Zoo definitely gets my vote (and Port Lympne if you are into cats or primates). It is also very easy to get to on public transportation. Book a train online (I used Virgin Trains) from London Euston Station to Chester Station. There are a few hotels within a couple blocks of the station - I stayed at a very nice and reasonably priced Premiere Inn. From there it is a few blocks - maybe half a mile or so - to the central city bus depot. A straight 15 minute bus ride to the front gate at Chester Zoo.