I think the legality issue is if the animal is a native or domestic species you are fine.
If the animal is dangerous or exotic species then you might have issues with out a permit. Exotic species are only legal if special conditions are meet. The key is if you cannot find the animal in your local pet store, then most likely it is illegal to have. a Reputable pet store will let you know what animals are suitable for you legally and lifestyle wise.
I assume since armadillos are not native in the UK, having one as a pet is not legal. If you live in the south west United states, like for say Arizona, you would be okay owning a armadillo. Pit bull dogs legality varies from state to state, and its only because the animal have a bad stereotype, dogs are not vicious unless its owner teach it to be vicious. Any Cross species hybrid, such as a half pit bull half tiger is grossly illegal and would be breaking a number of laws including international laws on scientific ethics.