I am not proposing changing the spelling throughout to UK. This is not a US/UK fight it is an argument against changing facts.     

 ::::::In my opinion, if you are referring to a specific document (even if it is not a proper noun and not capitalised) you must use the actual name of the document.  So you should say, '...a UK driving licence', because that is what it is.  If you want to be consistent throughout then you would need to say '...a UK drivers license', which is a non-existent entity.