Can you export a cockatoo from Australia to England?

The answer is: yes, but with a permit

Explanation:

The export of cockatoos from Australia is strictly regulated under the Environment Protection and Biodiversity Conservation Act 1999 (EPBC Act). A permit is required to export any native Australian animal or plant, including cockatoos. The permit application process involves demonstrating that the export will not have a detrimental impact on the wild population of cockatoos in Australia, and that the cockatoo will be properly cared for in its new country of residence.