I'm not British, but I am a strong supporter of the British Monarchy who hopes to get British citizenship one day. And what I'm about to say may be colored by my own personal ideas, but I consider it to be very reasonable.
It depends what you define as "great." One one hand, Edward VIII, despite all of his faults, was someone who wanted to aid his subjects and actively fight the depression that lingered until the war period. Considering how much at odds he was with Stanley Baldwin, I'm surprised he managed to remain on the throne as long as he did. Yet again, this is an opinion colored by my own personal feelings about the role of a monarch and his duties and responsibilities. Edward wanted to be more then a figurehead. People adored him. People supported him in his decision to marry. From a modern perspective, this person is attractive to think about. A prince who defied conservative minds of his time and picked love over prestige and glory. The idea sounds romantic. This, of course, is if you ignore the fact that he may or may not have been a racist Nazi sympathizer. So be careful which sides of his character you try to glorify.
As far as Queen Elizabeth II goes, she's done her duty for decades, with barely any mistakes on her part. Despite all she's been through, she still seems to be the glue that holds Britain together in times of crisis. It gives people a sense of stability and tradition, without any negative connotations behind a role of a monarch. She may not be the most exciting or glamorous Queen, but her unyielding knack to get things right and keep a high approval rating isn't due to luck, I assure you.