(I will admit, this headcanon is much more disjointed than the other, and has less proof than the other one.)
Kingsman isn’t the only branch in the world. After all, there were only about 15 knights of the round table, and fewer active agents. They couldn’t protect the world. They’re all part of a larger organization, started during the war by Germans who were very disillusioned by what was going on around them. They named it Yggdrasil, thinking, “What better name for a group protecting the world than the Tree of Worlds, the Tree of Life?”
Harry was trained in Asia (likely China) in hand-to-hand combat. All the years he’s spent active have let him smooth out his fighting. Crosstraining is important - you learn your branch’s specialty, and then another branch’s specialty.
Kingsman’s specialty is high-class mannerisms (and amazing gadgets, courtesy of Merlin).
Merlin was originally trained in the now disbanded Irish-Scottish branch, whose specialty was languages. He crosstrained in Germany, who are known for their cool gadgets (they want Merlin, but he just laughs).
Roxy crosstrains in Japan, becoming a deadly lady assassin.
Merlin vetoes Eggsy’s request to crosstrain in explosives. He shudders to think what Eggsy would do.
Eggsy has many requests - the French branch (specializing in poisons and free running), the Chinese branch (upon whom Harry made an impression, so much so they want his protégé), the American branch (specializing in disguises), and several others.