Drambuie is not SUPERVISED by the london beis din, it is APPROVED, which is similar to the list system used in europe, meaning that the beis din know the ingredients and have checked them out, but have never actually been down to the factory.
The london beis din has two separate logos, the hebrew one is actually a hechsher, meaning that they have the level nichnas veyoitzei required by shulchan oruch, the english lettering means apprpoved.
London beis din was headed until a few years ago by the ga’on r’ chanoich ehrentrau, today it is headed by r’ menachem gelley, and rabbbi jeffrey conway is responsible for kashruth issues.