This is the current list:
Afton Red Rift Cave – Devon SS
Aveline’s Hole – Uni West England
Bagshawe Cavern – Eldon PC
Baker’s Pit Cave – Plymouth CG
Biddlecombe Caves – WAYA CC inc. ISG
Bridge Cave – West Sussex CC
Brightgate Cave – Masson CG
Carlswark Cavern – Darkside CMC
Charterhouse Cave – Charterhouse CC
Chartist Cave – Crickhowell CG
Cherry Tree Hole – York Uni CPC
Chudleigh Caves – Devon SS
Coral Cave – Axbridge CG
Crackpot Cave – North of Tyne SA
Crescent Pot – Durham Uni SA
Critchlow Cave – Birmingham Cave & Crag
Cuckoo Cleeves – Frome CG
Dallimore’s Cave – Eagles CC
Darfar Pot – Darfar PC
Drunkard’s Hole – LADS CG
Ease Gill Caverns – Red Rose CPC
East Twin Swallet – S Bristol SS
Eastwater Cavern – Bristol EC
Eldon Hole – Eldon PC
Etches Cave (Upper Dove) – Iain Barker
Excalibur Pot – York CC
Fairy Cave Quarry – Fairy Caves MC
Flower Pot – Southampton UCC
Foxes Hole – Charterhouse OEC
G.B. Cave – Charterhouse CC
Gavel Pot – Kendal CC
Giant’s Hole – Eldon PC
Gibbets Brow Shaft – Shepton Mallet CC
Goatchurch Cavern – S Bristol SS
Great Douk Cave – West Lancs Scouts CT
Great Masson Cavern – Masson CG
Heron Pot – Morley PC
Higher Kiln Quarry Caves – Wm Pengelly CST
Hillocks Mine/Knotlow Cavern – Orpheus CC
Holme Bank Chert Mine – Stanley Head OEC
Holwell Cavern – Yeovil College CG
Hooe Lake Caves – Plymouth CG
Hunters’ Hole – Andy Sparrow
Hunters’ Lodge Inn Sink – Bristol EC
Kitley Caves – Yealmpton CC
Ladyside Pot – Darfar PC
Lancaster Hole – Red Rose CPC
Lathkill Head Cave – Birmingham Cave & Crag
Lesser Garth Cave – Isca CMC
Lionel’s Hole – Broad Pln/Woodside CC
Little Douk Pot – West Lancs Scouts CT
Little Neath RC – Croydon CC
Llethrid Swallet – Welsh Scout CCG
Llygad Llwchwr – Teifi Valley CG
Longwood/August – Mendip CG
Lost John’s Cave – Rubber Duck CC
Loxton Cave – Axbridge CG
Main’s Barn, Priddy – Cotham CG and WAYA CC inc ISG
M,anchester Hole – Black Sheep Diggers
Mangle Pot – South London Underground Soc
Manor Farm Swallet – Exeter UCC
Marble Steps Pot – Oxford UCC
Maskhill Mine – Eldon PC
Nancy Camel’s Hole – Mendip CG
Napps Cave – Bideford CCCC
Near Cliff Wood Rift – Doncaster Hallcross Moles SC
Ogof Draenen – Morgannwg CC
Ogof Fechan – Brighton EC
Ogof Ffynnon Ddu – South Wales CC
Ogof Hen Ffynhonau – North Wales CC
Ogof Hesp Alyn – North Wales CC
Ogof Llanymynech – Shropshire Scouts CT
Ogof Pen Eryr – Masons Arms CC
Ogof Pwll Swnd – Hereford CC
Old Ing Cave – Whitehough OEC
Otter Hole – Gloucester SS, Hades CC and Royal Forest Dean CC
Owl Hole – Orpheus CC
Oxlow Caverns – Eldon PC
P8 – Rubber Duck CC
Pant Mawr Pot – Westminster SG
Peak Cavern System – Technical SG
Penyghent Pot – Bradford PC
Pierre’s Pot – Bishop Fox’s School
Pikedaw Calamine Caverns – Yorkshire SS
Pinetree Pot – Mendip CG
Porth yr Ogof – Croydon CC
Pridhamsleigh Cavern – Devon SS
Pulpit Hole – Kent UCC
Pwll Dwfn – Gagendor CG
Radford Cave – Plymouth CG
Read’s Cavern – Bristol Assault Team
Red Moss Pot – Burnley CC
Redhouse Swallet – Gloucester SS
Redhurst Swallet – Darfar PC
Reed’s Cave – Wm Pengelly CST
Rhino Rift – Charterhouse CC
Riverside Swallet – Darfar PC
Rod’s Pot/Bath Swallet – SCG
Rowter Hole – Sheffield USS
Runscar Cave – Whitehough OEC
St Cuthbert’s Swallet – Bristol EC
St Dunstan’s Well Cave – Cerberus SS
Sell Gill Holes – Craven PC
Short Drop Cave – Kendal CC
Shute Shelve Cavern – Axbridge CG
Sidcot Swallet – Mendip OP
Singing River Mine – Young Expl CG
Slaughter Stream Cave – Royal Forest Dean CC
Stoke Lane Slocker – Cerberus SS
Storr Common caves – Black Rose CC
Sunset Hole – Sheffield USS
Swildon’s Dry Ways – Uni West England
Swildon’s Hole – Wessex CC
Tatham Wife Hole – Cambridge UCC
Tearsall Pipe Caverns No. 2 – Masson CG
Thistle Cave – Whitehough OEC
Thrupe Lane Swallet – SCG
Tyning’s Barrows Swallet – Shepton Mallett Caving Club (SMCC)
Upper Flood Swallet – Mendip CG
Water Icicle Close Cavern – Orpheus CC
Waterwheel Swallet – Cheddar CC
West Kingsdale Master Cave – ULSA
White Pit – Bristol EC
Total: 121 sites have been adopted by 83 clubs
Black sheep diggers are presumably members of other clubs, whilst UWE, crickhowell, north of tyne, eagles, darfar (several caves), LADS, Yeovil college, yealmpton, isca, broad plain / Woodside, Welsh scouts, teifi valley, cotham, south London, Bideford, Doncaster, Morgannwg, Shropshire scouts, masons arms, bishop fox's school, Bristol assault team and young explorers are no longer BCA members (although some may exist under different names or just not be paid up), not sure about charterhouse, Stanley head & whitehough OECs (which exist but do they still have keen cavers?), I don't know who SCG & WAYA inc. ISG are / were (bold just to make names easier to read)