Somehow missed this thread - my total is rather more modest than that held by some on the forum, but here goes - only doing species level, however, and omitting feral/domestic:
Red-necked wallaby, Notamacropus rufogriseus
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European hedgehog, Erinaceus europaeus
European mole, Talpa europaea
Common shrew, Sorex araneus
Eurasian pygmy shrew, Sorex minutus
Eurasian water shrew, Neomys fodiens
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Daubenton's bat, Myotis daubentonii
Common noctule, Nyctalus noctula
Serotine, Eptesicus serotinus
Common pipistrelle, Pipistrellus pipistrellus
Soprano pipistrelle, Pipistrellus pygmaeus
Schreibers' bat, Miniopterus schreibersii
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European rabbit, Oryctolagus cuniculus
European hare, Lepus europaeus
Mountain hare, Lepus timidus
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Red squirrel, Sciurus vulgaris
Grey squirrel, Sciurus carolinensis
European souslik, Spermophilus citellus
Eastern chipmunk, Tamias striatus
European beaver, Castor fiber
Bank vole, Myodes glareolus
European water vole, Arvicola amphibius
Field vole, Microtus agrestis
Brown rat, Rattus norvegicus
Black rat, Rattus rattus
Wood mouse, Apodemus sylvaticus
Striped field mouse, Apodemus agrarius
Eurasian harvest mouse, Micromys minutus
House mouse, Mus musculus
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Red fox, Vulpes vulpes
European otter, Lutra lutra
European pine marten, Martes martes
European badger, Meles meles
Stoat, Mustela erminea
European polecat, Mustela putorius
Least weasel, Mustela nivalis
South American coati, Nasua nasua
Grey seal, Halichoerus grypus
Common seal, Phoca vitulina
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Iberian ibex, Capra pyrenaica
Roe deer, Capreolus capreolus
Red deer, Cervus elaphus
Sika deer, Cervus nippon
Chinese water deer, Hydropotes inermis
Chinese muntjac, Muntiacus reevesi
Fallow deer, Dama dama
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Short-beaked common dolphin, Delphinus delphis
Bottle-nosed dolphin, Tursiops truncatus
Common porpoise, Phocoena phocoena
Cuvier's beaked whale, Ziphius cavirostris
Common minke whale, Balaenoptera acutorostrata
Humpback whale, Megaptera novaeangliae
Red-necked wallaby, Notamacropus rufogriseus
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European hedgehog, Erinaceus europaeus
European mole, Talpa europaea
Common shrew, Sorex araneus
Eurasian pygmy shrew, Sorex minutus
Eurasian water shrew, Neomys fodiens
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Daubenton's bat, Myotis daubentonii
Common noctule, Nyctalus noctula
Serotine, Eptesicus serotinus
Common pipistrelle, Pipistrellus pipistrellus
Soprano pipistrelle, Pipistrellus pygmaeus
Schreibers' bat, Miniopterus schreibersii
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European rabbit, Oryctolagus cuniculus
European hare, Lepus europaeus
Mountain hare, Lepus timidus
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Red squirrel, Sciurus vulgaris
Grey squirrel, Sciurus carolinensis
European souslik, Spermophilus citellus
Eastern chipmunk, Tamias striatus
European beaver, Castor fiber
Bank vole, Myodes glareolus
European water vole, Arvicola amphibius
Field vole, Microtus agrestis
Brown rat, Rattus norvegicus
Black rat, Rattus rattus
Wood mouse, Apodemus sylvaticus
Striped field mouse, Apodemus agrarius
Eurasian harvest mouse, Micromys minutus
House mouse, Mus musculus
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Red fox, Vulpes vulpes
European otter, Lutra lutra
European pine marten, Martes martes
European badger, Meles meles
Stoat, Mustela erminea
European polecat, Mustela putorius
Least weasel, Mustela nivalis
South American coati, Nasua nasua
Grey seal, Halichoerus grypus
Common seal, Phoca vitulina
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Iberian ibex, Capra pyrenaica
Roe deer, Capreolus capreolus
Red deer, Cervus elaphus
Sika deer, Cervus nippon
Chinese water deer, Hydropotes inermis
Chinese muntjac, Muntiacus reevesi
Fallow deer, Dama dama
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Short-beaked common dolphin, Delphinus delphis
Bottle-nosed dolphin, Tursiops truncatus
Common porpoise, Phocoena phocoena
Cuvier's beaked whale, Ziphius cavirostris
Common minke whale, Balaenoptera acutorostrata
Humpback whale, Megaptera novaeangliae