The 1936 British Olympic team had several Canadian born and trained players on it (all but 2 actually). Prior to the 1948 Olympics, the citizenship rules as set out by the IOC were very different based on a different political climate that was around the world, so a Canadian could go to Britain, get citizenship within 90 days (because he was born in the Commonwealth and the Commonwealth was there simply for Britain to exploit at the time). With the 1948 Winter Olympics, the IOC re-visited their citizenship rules due to the emergence/disappearance of countries, etc
No British trained player has played a regular season NHL game to date. Tony Hand of Scotland played in a couple of exhibition games in 1986 for the Edmonton Oilers and scored 7 points (and scored 8 points in 3 WHL games with the Victoria Cougars before deciding that the NHL was not for him).
45 British players have played in the NHL with Stockport, England's Steve Thomas the leading point getter with 933 points., Scotland's Charlie Gardiner was the first European born captain to win the Stanley Cup in 1934, and along with England's Joe Hall (the first European born player to play in the NHL, the first NHL player to die, and the only individual responsible for the cancellation of a Stanley Cup tournament) the only two Briton's in the Hockey Hall of Fame.