As the law now stands, any equine that is going to be residing in the UK for 30 days or more will need to be registered with a Defra-approved UK Passport Issuing Organisation (PIO), which will in turn update the Central Equine Database (CED).
Although you can technically do this with any UK PIO, there may be a UK representative which is close to or the same as your horse's breed/type that you may wish to choose - but the choice is yours.
The following is a link to all the current PIOs, both Studbook and ID only, with whom you can register:-
https://www.gov.uk/government/publications/horse-passport-issuing-organisations
However, there are a few exceptions to the 30 day rule for competition and breeding animals that will be here temporarily, but for longer than 30 days. For these we advise checking with Defra Equine Policy team directly.
The email address for the Equine Policy Team is:
Equine.Identification@defra.gov.uk