Eurasian red fox
Eurasian red squirrel
Eurasian roe deer
Brown rat
House mouse
Harbor seal
Birds
Common buzzard
Black kite
Barn owl
Common pheasant
Tufted duck
Barnacle goose
Mallard
Mute swan
Northern shoveler
Egyptian goose
Canada goose
European white stork
Western cattle egret
Little egret
Eurasian spoonbill
Great cormorant
Eurasian oystercatcher
Northern lapwing
Pied avocet
Lesser black-backed gull
European herring gull
Grey heron
Barn swallow
Ring-necked parakeet
African elephant
Ash-grey mouse
Australian fur seal
Australian green tree frog
Australian kestrel
Australian king parrot
Australian magpie
Australian pelican
Australian raven
Australian water dragon
Australian water rat
Australian wood duck
Azure kingfisher
Black-breasted buzzard
Black rat (feral)
Black swan
Blue groper
Blue-billed duck
Blue Mountains tree frog
Brolga
Brown falcon
Brown goshawk
Brown rat (feral)
Bull ray
Bush rat
Bush turkey
Cane toad (feral)
Cape Barren goose
Cattle egret
Chestnut teal
Chuditch
Cockatiel (escaped pet no doubt in suburban Sydney, surprised corvid or raptor bird hadnt gotten it yet)
Common Sydney octopus
Common brushtail possum
Common hippopotamus
Common ringtail possum
Common stingaree
Common wallaroo
Common wombat
Crab-eating macaque
Crested pigeon
Crimson rosella
Diamond python
Domestic goat (feral)
Domestic horse (feral)
Dugite
Eastern blue-tongued lizard
Eastern dward tree frog
Eastern grey kangaroo
Eastern long-necked turtle
Eastern rosella
Eastern short-neck turtle
Emu
European rabbit (feral)
Fiddler ray
Galah
Giraffe
Green and golden bell frog
Green sea turtle
Grey butcher bird
Grey-headed flying fox
Hardhead duck
House mouse (feral)
Indo-Pacific bottle-nosed dolphin
Jacky dragon
Javan rusa deer (feral)
King quail
King skink
Lace monitor
Laughing kookaburra
Little corella
Little penguin
Little pied cormorant
Little red flying fox
Mainland tiger snake
Malleefowl
Marbled gecko
Motorbike frog
Musk Duck
Mute swan
Nankeen night-heron
New Zealand fur seal
Oblong turtle
Offsprey
Ostrich
Pacific black duck
Peregrine falcon
Peron's tree frog
Plains zebra
Port Jackson shark
Quokka
Rainbow lorikeet
Red fox (feral and also wild in UK)
Red-bellied black snake
Red-tailed black cockatoo
Royal spoonbill
Shingleback lizard
Short-beaked echidna
South-eastern black rhinoceros
Southern African lion
Southern boobook owl
Southern brown bandicoot
Southern eagle ray
Southern leaf-tailed gecko
Sulphur-crested cockatoo
Superb fairy-wren
Superb lyrebird
Swamp wallaby
Tammar wallaby
Tawny frogmouth
Vervet monkey
Waterbuck
Wedge-tailed eagle
Western blue-tongued lizard
Western brush wallaby
Western grey kangaroo
Whistling kite
Wille wagtail
Wobbegong shark
Yellow-tailed black cockatoo
(think some insect species and some other bird species like terns, and fish species too)
+ red deer (if Richmond Park outside London counts), satin bowerbird and other birds , redback spider and other spiders think like an orb-weaver species, some fish and insects and invertibrates (sea urchins, starfish, jellyfish etc)
A few additions since I last replied to this thread
MAMMALS
Short-beaked Echidna
Platypus
Common Wombat
Koala
Krefft's Glider
Common Brushtail Possum
Quokka
Eastern Grey Kangaroo
Western Grey Kangaroo
Swamp Wallaby
Red-necked Wallaby
Agile Wallaby
Red-legged Pademelon
Lumholtz' Tree-Kangaroo
European Rabbit
Japanese Macaque
Spectacled Flying-fox
Black Flying-fox
Grey-headed Flying-fox
Pig
Indo-Pacific Bottlenose Dolphin
Sika Deer
Longnose Fur Seal
BIRDS
Southern Cassowary
Magpie-goose
Plumed Whistling-Duck
Wandering Whistling-Duck
Black Swan
Radjah Shelduck
Mandarin Duck
Gadwall
Eurasian Wigeon
Pacific Black Duck
Eastern Spot-billed Duck
Mallard
Chestnut Teal
Tufted Duck
Blue-billed Duck
Australian Brushturkey
Helmeted Guineafowl
Japanese Green Pheasant
Indian Peafowl
Little Grebe
Rock Dove
Brown Cuckoo-Dove
Pacific Emerald-Dove
Peaceful Dove
Bar-shouldered Dove
Nicobar Pigeon
Wompoo Fruit-Dove
Superb Fruit-Dove
Rose-crowned Fruit-Dove
Torresian Imperial-Pigeon
Topknot Pigeon
Eastern Koel
Tawny Frogmouth
Papuan Frogmouth
Buff-banded Rail
Australasian Swamphen
Sarus Crane
Brolga
Bush Stone-curlew
Pied Stilt
Whimbrel
Black-headed Gull
Bridled Tern
Little Penguin
Black-necked Stork
Australian Pelican
Great Egret
Plumed Egret
Eastern Cattle Egret
Little Egret
Royal Spoonbill
Yellow-billed Spoonbill
Pacific Baza
Wedge-tailed Eagle
Whistling Kite
Eastern Barn Owl
Laughing Kookaburra
Blue-winged Kookaburra
Forest Kingfisher
Rainbow Bee-eater
Peregrine Falcon
Yellow-tailed Black-Cockatoo
Red-tailed Black-Cockatoo
Galah
Sulphur-crested Cockatoo
Regent Parrot
Red-winged Parrot
Australian Ringneck
Double-eyed Fig-Parrot
Purple-crowned Lorikeet
Musk Lorikeet
Rainbow Lorikeet
Great Bowerbird
Helmeted (Hornbill) Friarbird
White-browed Scrubwren
Eastern Whipbird
Australasian Figbird
Azure-winged Magpie
Coal Tit
Warbling White-eye
Crimson Finch
Scaly-breasted Munia
Chestnut-breasted Mannikin
Brambling
HERPS
Green Tree Frog
White-lipped Tree Frog
Southern Brown Tree Frog
Eastern Dwarf Tree Frog
Northern Leaf-tailed Gecko
Common Bluetongue
Lace Monitor
Boyd's Forest Dragon
Australian Water Dragon
Carpet Python
Brown Tree Snake
Common Tree Snake
Common Keelback
Olive Sea Snake
Tiger Snake
Eastern Short-necked Turtle
Pond Slider
Green Sea Turtle
Loggerhead Sea Turtle
Saltwater Crocodile