With a POD whenever you want, have it so that, at some point in the nineteenth century, the British monarch is restored to being head of government as well as head of state.
Napoleon invades successfully and has Parliament dissolved. George III is forced to the negotiation table and is told that he will be permitted to keep his kingdom in exchange for ending the war on France, giving several colonies, limiting the size of the Navy, and a marriage of Princess Charlotte to a Bonaparte at some point in the future. Napoleon then doesn't invade Russia, everything goes as planned, and the British people are ruled by a Bonaparte King of England after he and Princess Charlotte successfully have fifteen children, all of whom survive to adulthood.
Couldn't such a thing just break George's mind and render him incapable of negotiation?
A much more likely scenario considering his mental fragility.
That said, such a scenario is hard but not impossible. Basically you need to discredit the major parties to the point that restoring the Monarch's former power seems to be a good idea or the only solution. It would also help if the monarch is highly respect by the country at large, like Queen Elizabeth is today. The problem becomes how to discredit the parties. Some kind of massive scandal would be necessary, maybe involving taxation or attempted collaboration with a foreign power? Perhaps some kind of national emergency, an invasion like Beausoleil suggested, though without the collaboration with the Bonapartes. That's more likely to discredit the monarchy rather than the ruling parties.