There is confusion here on your part. From what you have told us you do not have a EASA licence, you have a ICAO compliant UK PPL. It doesn't matter, since January 1st 2021 that the licence still has the words EASA on the front cover, this must now be ignored. So, for your UK ICAO PPL to be valid then you must also hold a UK ICAO standard Class 2 medical issued by a UK CAA approved AME. No other medical will do including your Spanish issued EASA Class 2. In short, you need therefore to obtain a UK Class 2 medical to support your UK licence. The Spanish EASA Class 2 medical you now have will support your EASA licence when you eventually gain one. This is how it works throughout the world.
Your change of address is a different matter. There is no need to have a current medical nor a class rating to update you licence contact address. To change your address simply complete the appropriate UK CAA change of address form.