First, British history goes back to before most other nations formed. While most of Europe was part of the Holy Roman Empire, the British Isles were not. Instead the countries that now form the United Kingdom were already established. So, there is much history available to tell the tale of such long standing countries as now form the United Kingdom.
As for the Royal Mint, well it has been around for well over a thousand years, perhaps not in its current location, but the Royal Mint was established in the tenth century. Over this expanse of time the Royal Mint has had much experience in striking coins, and has developed a reputation as being a mint that produces high quality pieces.