The College of Arms' jurisdiction is England, Wales and Northern Ireland, and any other commonwealth realm that hasn't set up its own heraldic authority (Canada has - the Canadian Heraldic Authority under the Chief Herald of Canada). The College of Arms also grants arms to individuals of English etc descent living in countries with no heraldic authority - principally to Americans.

Note the lack of Scotland from its jurisdiction. That comes under the Lord Lyon King of Arms. Whereas the English heraldic enforcement authority, the Court of Chivalry, is virtually moribund (hasn't sat since the 1950s), the Lyon Court is very much an active court with its own procurator-fiscal (prosecutor in Scots law).

When BA adopted the Landor livery in the 80s, it was noticed that BA's grant of arms from the College of Arms had never been "matriculated" with the Lyon Court, which meant it was illegal to use and display the arms in Scotland. The story I heard (which may be apocryphal, but which I heard directly from the man who noticed the discrepancy and notified the Lyon Court about it) was that the Lyon Court threatened to send men with sledgehammers to GLA and EDI to physically destroy the illegal arms on the BA aircrafts' tailfins, unless BA promptly coughed up the Lord Lyon's matriculation fee. BA did.