To run a business selling pet animals you need to apply for a licence [pdf] 144KB and pay the animal licensing fees 2017-18 [pdf] 56KB. This includes all commercial selling of pet animals, including pet shops and businesses selling animals over the internet.
There are strict guidelines and conditions applied to the licence [pdf] 91KB to ensure the health, safety and welfare of all the animals.
Pet shops are also required to meet the requirements of the Animal Welfare Act 2006. More information can be found in the pet vending licensing 2013 model conditions [pdf] 404KB.