But , the Duchies did not want to be joined to Great Britain , so their constitutions constitutions stopped the King and heir apparent of Great Britain from becoming Duke if other eligible male heirs exist . . Therefore after Edward , Prince of Wales was his next brother , Alfred , Duke of Edinburgh . However , the constitutions of both duchies excluded the British heir apparent from the ducal thrones if there were other eligible male heirs , although Albert Edward , Prince of Wales had already renounced his claim to the ducal throne in favor of his next brother , Prince Alfred , Duke of Edinburgh .