No, Assistance Dogs UK are so called 'registered' (no register actually exists) but actually, dogs trained by ADUK-registered organisations are legal, as are organisation trained dogs outside of ADUK, as are completely independently owner-trained Assistance Dogs. As long as you have a disability as is defined in the Equality Act 2010 and the dog fulfils the criteria in the Equality Act 2010, that it does 3 tasks and is up to standard (ADI PA test) in public access then they are legally an Assistance Dog in the law. So no 'register' exists as such and dogs trained outside the ADUK/ADI registered organisations aren't any more legal than a dog trained by its owner. Hope this helps.

Legally, any dog trained to Assistance Dog standard whether charity-trained or self/owner-trained is covered under the Equality Act. Molly was trained by me but with help from an Assistance Dogs UK charity, Dog A.I.D. but I could've completely trained her myself independent from them and still been covered under the Equality Act. As long as the dog does a minimum of 3 tasks (and emotional support is not a task) and is trained to the accepted public access standard then the dog is covered.