Oh, well as Scott said, you need to thoroughly, and I mean thoroughly research what is required by the UK (specific Country you are taking him into) to bring a parrot into whatever specific country you are bringing him into. The rules and requirements are completely different for every country. However, for this specific purpose, they usually require, and I'd be my life on it that they will, a "Certificate of Health" from an Avian Vet that is just recent, dated, lists you as the owner, and says that he has been fully examined by an Avian Specialist Vet, and that he is healthy and possesses no current illnesses or infections. This document will most-definitely be required regardless of the proof-of-ownership requirement, as I've not ever seen a country in the world that didn't require it, especially with birds. However, this document may very well also serve as your proof-of-ownership document too, as it will list you as the bird's owner. So I'd be finding a Certified Avian Vet and making an appointment for him, and be sure to tell them when you make the appointment why you are doing it and what you need. And before you take him to his vet appointment, call the authorities in the specific country you are wanting to move him to, and ask THEM specifically what they are going to require at the border/airport, as that is what matters, not what your local authorities in the country you're in now are telling you. And be sure to start this process of collecting the documents now, well before you are planning to move. And ask them how recent the Certificate of Health needs to be to the date you plan to bring him into the country, so that you can make the Avian Vet appointment accordingly...
***By the way, and I hate to be "that person" but I'm going to be anyway...Just because your bird has "always been healthy" does not at all mean that you should not be taking him to a Certified Avian Vet or an Avian Specialist at least once yearly for a Wellness Exam that includes a Fecal Culture and standard, routine, baseline blood-work. In fact, it means just the opposite. All birds possess an innate survival instinct to hide all outward signs and symptoms of illness, injury, and pain for as long as they possibly can; this is a survival instinct that protects them and their flockmates from predators, and keeps them from being kicked-out of the flock for fear of appearing weak to predators. As such, most pet parrots just instinctively hide all outward signs of illness and pain for as long as possible, usually this equates to months and months, if not longer. So by the time we as people recognize that our birds are sick, that something is wrong with them, they've typically been sick for months and months, and it's often too late to help them. This is why something as simple as a bacterial or fungal infection in their Gastrointestinal Tracts, that could easily be treated with a simple round of Antibiotics or Anti-Fungal medications IF caught within a reasonable amount of time, end-up often killing pet parrots, because by the time their owners notice that something is wrong with them, the infection has spread to their bloodstream and they have become septic. So taking your parrot to either a Certified Avian Vet or an Avian Specialist at least once a year for a complete Wellness-Exam that includes at least a Fecal Culture and baseline blood-work that you can use as the comparison each year to gauge his overall-health and the development of serious diseases that you cannot see until they are too far-gone to do anything about, such as liver and kidney diseases, heart conditions and diseases, and Respiratory conditions including diseases of their very important Air-Sac systems is so very important. The number one reason that most captive, pet parrots do not live their full life-span is because they are not taken yearly for a Wellness Exam with blood work...