It would be reasonable for the UK CAA to charge a small conversion fee for that (i.e. issuing a new UK CAA license).
WHY? what on earth has that got to do with safe operation? If a Brazilian pilot goes to a UK club he will be checked out to their satisfaction. Having an unnecessary piece of papers serves no useful purpose. The UK has complied with ICAO Annex 1 in both spirit and practice unlike many other countries. It has not caused any safety issues in doing so.
1.2.2.2 Recommendation.— A pilot licence issued by a
Contracting State should be rendered valid by other
Contracting States for use in private flights.
As far as Airr Law exams are concerned. they ceased having any relevance to flying an aeroplane years ago.