Your best bet is to use Zootierliste. Here is a link,
ZootierlisteHomepage you can choose between the three Pinniped lists (Eared Seals, Walruses and Earless Seals). Zootierliste will list which zoos have which species, and will also list the rest of Europe.
It is the simplest, and quicket way to answer your question.
EDIT: So in answer to your question, the species kept in the UK and which zoos have them are listed below:
Californian Sea Lion:
Bewdley (West Midland Safari Park)
Blackpool (Zoo)
Chessington (Sea Life)
Chessington (World of Adventures - bis 1987 Zoo)
Dunstable (Whipsnade Wild Animal Park)
Gweek (National Seal Sanctuary)
Ilfracombe (Combe Martin Wildlife)
Knowsley (Safari Park)
Longleat (Safari Park)
Lowestoft (Pleasurewood Hills Leisure Park)
Malton (Flamingo Land)
Stirling (Blair Drummond Safari Park and Adventure Park)
Woburn (Safari Park)
Belfast (Zoo)
Colwyn Bay (Welsh Mountain Zoo)
Cape fur seal:
Diss (Banham Zoo)
Gweek (National Seal Sanctuary)
Rhyl (SeaQuarium)
South American fur seal:
Bristol (Zoo)
Torquay (Living Coasts)
South American sea lion:
Colchester (Zoo)
Dudley (Zoo)
Gweek (National Seal Sanctuary)
Twycross (Zoo)
Edinburgh (Zoo)
Eastern Atlantic harbour seal:
Colchester (Zoo)
Gweek (National Seal Sanctuary)
Hunstanton (Sea Life Sanctuary)
Mablethorpe (Seal Rescue Centre)
Scarborough (Sea Life)
Skegness (Natureland Seal Sanctuary)
Tynemouth (Blue Reef Aquarium)
Weymouth (Sea Life)
Oban (Scottish Sea Life Sanctuary)
St. Andrews (St. Andrews Aquarium)
Rhyl (SeaQuarium)
Grey Seal:
Gweek (National Seal Sanctuary)
Hunstanton (Sea Life Sanctuary)
Mablethorpe (Seal Rescue Centre)
Scarborough (Sea Life)
Skegness (Natureland Seal Sanctuary)
Weymouth (Sea Life)
Colwyn Bay (Welsh Mountain Zoo)