Edward VIII refuses to abdicate

This seems quite of an unlikely scenario, since Edward was well aware that his marriage with Wallis Simpson wouldn't be accepted by the Church of England and a constitutional crisis would happen if he stays on the throne. But let's say for some reason Edward stubbornly remained as King. What would happen next? Would Parliament try to oust him if they can, or would he be allowed to stay? How would Edward's pro-appeasement stance affect the public opinion on the royal family on the long term?
A group of well-bred people will arrive at the Palace, present him with his abdication letter for signature and suggest some places that might offer sufficiently comfortable exile for him and his wife.

This would, of course, only happen after politely but indirectly expliaining how unpleasant it would all be if Parliament had to cut off his allowance and estates, pass a law to dethrone him (or find a suitable scandal from his past) and place a suitable candidate on the throne.