Oh yes, Iceland, the country famous for its endless forests (for timber), textile industry (for sails), dockyards, and ammunition factories. And also for its proximity to the English channel. Is this serious?
In much the same way that OTL Napoléon would, in 1815, rather face the black death than admit defeat, you mean? Well, if the Hanoverian family want to flee, good for them, but now it's them and what army? (to the point: how do they pay them without London ?) What arms factories, recruiting grounds, etc.? Note that with the South of England, Masséna is in control not only of the biggest part of the population and industry and the logistical hub, but also has in hand the officer academies, dockyards, etc. The typical Londoner merchant now has a choice between living under Masséna (and now being able to trade with the continent again, etc.) and joining the fleeing king (and not being paid for it, and soon getting killed by the, up to now, invincible French army). Most thoughts of rebelion will be very much procrastinated...
The Austrians, Prussians etc. capitulated for much less than this. (The Russians had a large, decentralized country, still 1 capital city remaining, and were supported by English gold; none of this apply to TTL Britain). Basically, once there was no longer a significant British army between Masséna and London, the Londoners are going to force their king to choose between negociating (as king of the United Kingdom) or fighting on (as king of Northern Ireland, maybe?).
If you really want to throw the French out, your better bet would be to first negociate and then stage some kind of Sicilian Vespers; however even this is so obvious that I cannot imagine Napoléon not taking some measures against it (obvious solution: royal hostages).
Your main POD was Gibraltar being a Franco-Spanish victory. How are France and Spain at war?