Where: The College of Arms
The coats of arms tradition dates back to the early medieval era, when knights wore these on helmets and shields to tell rivals apart in battles and tournaments. Once upon a time they could only be inherited, however today it's possible for anyone to apply (for a fee; plus things like awards help towards a successful application).
The College of Arms is the official authority responsible for granting these, along with registers of genealogies, Royal Licences, changes of name, and flags, and advises on peerages, honours and symbols like regional and national flags. The building housing the College of Arms dates back to the 1670s, and parts of it are open to the public - you'll be able to walk through the 18th century Earl Marshal's Court (essentially the chief exec of the College) and check out portraits of past Officers of Arms.