This question was inspired by another question on animals in the Harry Potter world. That question was about animals that were half-magical and half-muggle.
Which animals that look and act mugglish (is that a word?) can interact with magical people, beasts, and places?
I am specifically not asking about truly magical creatures that had interacted with muggles incidentally. So that leaves out Thunderbirds, phoenixes, occamies, hippogriffs, dragons, and other such beasts.
I am asking about animals like owls which can fly from a magical place like Hogwarts to a muggle place like London and back.
Can other muggle creatures go from the muggle world to the magical world and back?
Edit to clarify: I am not asking about situations where somebody brings an animal to a magical place, such as when Neville brings his toad, Trevor, to Hogwarts. I asking about where animals can freely interact with both magical and muggle places on their own. We know muggle humans can't, because otherwise they would see Hogwarts or enter Platform 9 3/4. But we don't see incidents in the stories where muggle animals try to go to magical places on their own and are prevented from doing so because of charms and spells.
Edit to clarify: Although an animagus like Peter Pettigrew can transform into a rat and go from magical places to muggle places, I am only asking about normal animals. It seemed obvious to me that animagi could go where they wish in either human or animal form. (Thanks to Reya for pointing that out.)