I've had a look at Zootierliste and below is a list of mammal species in 10 or more UK collections. Please note that Zootierliste lists domestic varieties and 'species' under a separate category and I haven't included them here:
83: Meerkat
69: Oriental small-clawed otter
59: Ring-tailed lemur
57: Red-necked wallaby
49: Black and white ruffed lemur
41: Common marmoset
37: Capybara
36: Ring-tailed coati
34: Cotton-top tamarin, mara, tiger
32: Lion, fallow deer
31: Red ruffed lemur
27: Northern raccoon, Brazilian tapir
25: Giraffe
23: Emperor tamarin, Goeldi’s monkey, Geoffroy’s and pygmy marmosets, red squirrel, Siberian chipmunk, red panda
22: Reeve’s muntjac
21: Lar gibbon, northern lynx, common zebra
20: White-faced saki, black-capped capuchin, common squirrel monkey, Azara’s agouti, long-tailed chinchilla
19: Crested porcupine, wolf, red river hog
18: Parma wallaby, South African porcupine, degu, striped skunk
17: Lesser hedgehog tenrec, yellow mongoose, leopard, cheetah
16: California sea-lion, red deer
15: Egyptian rousette bat, red-bellied lemur, golden lion tamarin, silvery marmoset, European harvest mouse, Gambian giant pouched rat, dwarf mongoose, snow leopard, white rhinoceros, sitatunga
14: Rodriguez flying fox, Colombian black howler monkey, golden-headed lion tamarin
13: Belanger’s tree shrew, black lemur (including blue-eyed lemur), red-fronted lemur, black-and-gold howler, golden-handed and red-bellied tamarins, siamang, chimpanzee, two-toed sloth, ocelot, serval, sika, bongo
12: Long-nosed potoroo, guereza, giant anteater, lechwe
11: Sulawesi crested macaque, western gorilla, Prevost’s squirrel, African wild dog, red fox, North American and Eurasian river otters, axis deer, scimitar-horned oryx, blackbuck
10: Four-toed hedgehog, Alaotran gentle lemur, Bolivian squirrel monkey, pied tamarin, Asia Minor spiny mouse, fennec, vicuna
There are some suprises here, but it does seem that many of the species are kept for reasons other than conservation.
The following species only exist in only 1 UK zoo
Short-beaked echidna, bear cuscus, koala, agile wallaby, Goodfellow’s tree kangaroo, European mole, Pallas’s long-tongued bat, Indian, little red and Lyle’s flying foxes, straw-coloured fruit bat, eastern grey bamboo, white-collared brown and western fat-tailed dwarf lemurs, northern dry zone slender loris, Moholi bushbaby, eastern tarsier, black-faced and black-headed spider monkeys, silvery woolly monkey, southern Bolivian night monkey, black crested and golden-bellied mangabeys, bonnet and Heck’s macaques, olive baboon, crowned, mona, lesser spot-nosed, Lowe’s, Roloway and red-tailed guenons, Javan and mitred surelis, purple-faced langur, bonobo, Hoffman’s sloth, little hairy and nine-banded armadillos, black-tailed, edible and Kellart’s dwarf dormice, grizzled giant and red-bellied squirrels, red and white giant and southern flying squirrels, Brazilian porcupine, rock cavy, black-rumped agouti, mountain and plains viscachas, Desmarest’s hutia, greater Egyptian jerboa, Russian dwarf and Syrian hamsters, steppe lemming, Nicaraguan harvest mouse, Arabian and Mount Kulal spiny mice, Egyptian gerbil, common water rat, Matthey’s, Natal multimammate and yellow-necked field mice, North Luzon giant, Panay bushy-tailed cloud rat, African civet, banded palm civet, marsh and ring-tailed mongooses, spotted fanaloka, brown and spotted hyenas, black-footed cat, little spotted and jungle cats, jaguarondi, American black bear, giant panda, sloth bear, white-nosed coati, ratel, marbled polecat, Siberian weasel, harbour and hooded seals, bearded pig, white-lipped peccary, tufted deer, caribou, Bawean deer, Javan rusa, Persian fallow deer, wapiti, gaur, Arabian oryx, Arabian mountain gazelle, red duiker, musk ox, Chinese goral, Japanese serow, bharal, markhor, Himalayan tahr