RSPCA inspectors have recently found lynx - types of wild cats - kept in sheds and dangerous snakes in the same house as a newborn baby.
And Louis the five-foot long Mississippi alligator was discovered living in a pond liner in a very cramped bedroom.
Inspector Ian Briggs said: "Alligators like Louis can grow up to 12 feet in length. Clearly, a flat is a totally unsuitable environment for an animal such as this."
But because Louis' owner had no licence for him, the RSPCA could not keep an eye on his living conditions.
The animal charity hopes the suggestions they're making to the government will improve the conditions in which animals are kept and public safety.