According to Zootierliste the following UK zoos have wild cats:
Ashford: Puma, fishing cat, northern lynx, ocelot, Pallas' cat, serval, rusty-spotted cat, tiger, clouded leopard, jaguar, lion, leopard, snow leopard, cheetah
Ballaugh: Northern lynx
Banham: Geoffroy's cat, ocelot, Pallas' cat, tiger, snow leopard, cheetah, lion
Bassenthwaite: Fishing cat, northern lynx, serval
Begelly: Ocelot
Belfast: Asian golden cat, lion, cheetah, tiger
Birmingham: Northern lynx, ocelot
Blackpool: Lion, tiger
Blair Drummond: Lion, tiger
Borth: Geoffroy's cat, northern lynx, ocelot, leopard
Bristol: Sand cat, lion
Broxbourne: Puma, ocelot, Pallas' cat, northern lynx, leopard, snow leopard, cheetah, lion, tiger
Caldergelen: Wild cat
Camperdown: Wild cat
Canterbury: Northern lynx, wild cat
Chessington: Lion, leopard, tiger
Chester: Serval, lion, jaguar, cheetah, tiger
Chestnut Centre: Wild cat
Colchester: Geoffroy's cat, leopard, lion, tiger, cheetah
Colwyn Bay: Margay, snow leopard, tiger
Combe Martin: Lion, snow leopard
Comrie: Wild cat
Cotswold: Jaguarundi, Pallas' cat, leopard, lion, clouded leopard
Cromer: Puma, margay, ocelot, jaguar
Cupar: Northern lynx, wild cat
Dartmoor: Puma, serval, northern lynx, jaguar, lion, tiger, cheetah
Drayton Manor: Fishing cat, Geoffroy's cat, wild cat, northern lynx, leopard
Drusilla's: Serval
Dudley: Northern lynx, Geoffroy's cat, lion, tiger, snow leopard
Dundee: Northern lynx
Eagle heights: Cheetah
Edinburgh: Margay, serval, Asian golden cat, leopard, lion, jaguar, tiger
Exmoor: Sand cat, caracal, puma, fishing cat, leopard
Fife: Wild cat
Galloway: Leopard cat, northern lynx, wild cat, serval
Gentleshaw: Puma, northern lynx, wild cat
Hamerton: Jaguarundi, little tiger cat, serval, rusty-spotted cat, cheetah, tiger
Heythrop: Leopard, lion, tiger, snow leopard
Highland WP: Northern lynx, Pallas' cat, wild cat, tiger
Howletts: Wild cat, fishing cat, ocelot, Pallas' cat, serval, northern lynx, lion, clouded leopard, leopard, tiger, snow leopard
Kessingland: Serval, lion, cheetah
Knowsley: Lion, tiger
Linton: Leopard, clouded leopard, lion, tiger, snow leopard
London: Serval, lion
Longleat: Lion, tiger, cheetah
Mablethorpe: Northern lynx, wild cat
Malton: Northern lynx, lion, tiger
Marwell: Sand cat, ocelot, serval, leopard, tiger, snow leopard, cheetah
Milnthorpe: Snow leopard
New Forest: Northern lynx, wild cat
Newchapel: Wild cat
Newchurch: Geoffroy's cat, ocelot
Newquay: Northern lynx, fishing cat, lion
Paignton: Lion, cheetah, tiger
Polbeth: Wild cat
Porfell: Caracal
Port Lympne: Black-footed cat, caracal, northern lynx, fishing cat, wild cat, margay, ocelot, Pallas' cat, serval, rusty-spotted cat, lion, clouded leopard, tiger, snow leopard, cheetah
Reaseheath: Serval
Rutland: Puma, leopard
Sandown: Jaguar, lion, tiger
Shaldon: Ocelot
Shepreth: Puma, northern lynx
South Lakes: Lion, jaguar, tiger
Tamar: Wild cat
Thrigby Hall: Leopard cat, Asiatic golden cat, leopard, clouded leopard, snow leopard, tiger
Tropiquaria: Wild cat, serval
Twycross: Wild cat, leopard, snow leopard
West Midland: Lion, tiger
Whipsnade: Northern lynx, tiger, lion, cheetah
Wingham: Caracal, puma, wild cat, jaguar, lion, tiger
Woburn: Northern lynx, lion
Wraxall: Lion, tiger
Yorkshire: Leopard, lion, tiger
The UK zoos with the most cat species are:
Port Lympne: 15
Ashford: 14
Howletts: 11
Broxbourne: 9
Banham, Dartmoor, Edinburgh, Marwell: 7
Hamerton, Thrigby Hall, Wingham: 6
Chester, Colchester, Cotswold, Drayton Manor, Dudley, Exmoor, Linton: 5