The excellent book 'The Zoos of Great Britain and Ireland' by John Tuson has a section on the impressively long list of first UK breedings for mammals and birds that occurred at Bristol Zoo Gardens over the years. Not an exhaustive list of historic animals (like
@PossumRoach says, ZTL former holdings is your best bet for that), but a very useful and interesting resource that I feel is relevant enough to the matter at hand that I should post it.
Mammals:
1881 - Indian Grey Mongoose
1886~ - American Black Bear
1934 - Chimpanzee
1952 - Common Squirrel Monkey
1958 - Black Rhinoceros
1966 - Okapi
1968 - leucistic Tiger
1971 - Western Gorilla
1971 - Sumatran Orangutan
1978 - Linnaeus' Two-toed Sloth
1978 - Emperor Tamarin
1979 - Geoffroy's Tamarin
1979 - Persian Leopard
1982 - Red-fronted Lemur
1986 - Large Flying Fox
1989 - Allen's Swamp Monkey
1989 - Sumatran Tiger
1990 - South American Fur Seal
2006 - Merriam's Kangaroo-rat
2017 - Eastern Quoll
Birds:
1966 - Rufous-necked Wood-rail
1967 - Tasmanian Native-hen
1969 - Scarlet Ibis
1972 - Victoria Crowned-pigeon
1973 - Straw-necked Ibis
1973 - Burmeister's Seriema
1976 - Yellow-collared Macaw
1981 - Merrill's Fruit-pigeon
1982 - Green-and-white Zone-tailed Pigeon
1986 - Sulawesi Ground-dove
1988 - Chestnut-naped Imperial-pigeon
1992 - Peruvian Thick-knee
Not sure how many are also European or even captive first breedings, but I suspect a fair few are.
Looking at how common some of those species, such as the tamarins, gorilla or Scarlet Ibis, have become well-established in UK zoos, I suspect that BZG (which I should start calling it so as to distinguish from what is now known as 'Bristol Zoo Project') is in large part responsible for this.