Assuming a pod in the summer of 1805 puts this at a pretty interesting hinge point in the course of the Napoleonic Wars. Napoleon is yet to install any of his brothers on foreign thrones and we are still a few months from the miraculous success of the Ulm campaign and Austerlitz. My own personal reading of the historiography is that victory at Austerlitz and the Peace of Pressburg marks the departure of Napoleon from "the amount of egoism necessary to run an empire" to full-on megalomania.
On the other hand, getting divine winds and the capability to sweep the British army on their home turf probably speeds up that process. Napoleon has stated that he intended to declare England a republic, dissolve the House of Lords, expropriate the wealth of the royalty, free Ireland, and expel the monarchy. But it is hard to tell how much was just bitter blustering from a now-exiled emperor. As his troops march through London, Russia and Austria are likely gearing up to strike him on the continent. The most immediate action he would take is signing a harsh peace treaty with whatever provisional government has been set up. Freeing Ireland, occupying Portsmouth, taking several colonies, a massive indemnity, and banning the war party from participating in government.
If Austerlitz killed Pitt I imagine French troops landing on English shores would easily incapacitate him, but invasions still tend to unite a nation and I doubt even someone like Charles James Fox would willingly serve as a quisling. The British government planned to establish a temporary capital in the North. Napoleon let the Prussians and Austrians keep their kings, but it is harder for me to imagine the same happening for George III. And at this point in time, every one of Napoleon's relatives with the exception of Viceroy Eugene is freely available to take the thrones of Wales, Scotland, Ireland, Mercia, etc.
It is also notable that the largest annexations of the Napoleonic period (all of the Netherlands, Rome, Illyria, Hamburg, Catalonia, etc) were sparked by the continental system which is no longer necessary with Britain cowed. So Napoleon's mindset toward European governance is also completely changed.