To check if a waste carrier is registered in East Lothian, you should ask the waste carrier for their registration details and confirm their status by checking the SEPA public register. This will help ensure that your waste is handled by someone authorized to transport it.
You can check the registration here: SEPA Public Register.
It's important to conduct these checks to avoid sharing legal liability with unregistered waste carriers, especially if your waste ends up being fly-tipped.