Since British policy since the time of Elizabeth I has been to ensure the balance of power in Europe to prevent any single power form becoming dominant and thus threatening England proper, I would think the government would be working overtime to put that policy into effect and build a coalition to derail an ascendant France.
At home, this would lead to the invitation of anti-French exiles from across Europe to come to England, both to settle and bring their skills to England (much like French Huguenots were allowed to settle in England in the recent past in this time line), and to build up intelligence on the affected areas, develop alliances and even create mercenary forces to carry out actions on the periphery of France, around the world, or protect vulnerable points in Scotland and Ireland.
The social issues of allowing large numbers of foreigners in England would be mitigated to a certain extent to keeping them confined to London, Portsmouth and perhaps a few other large English cities, but there would still be social unrest, particularly as skilled tradesmen from the continent began taking business from other English tradesmen. OTOH, they might also be welcomed in low skill, highly dangerous jobs like coal mining and as crews on merchant shipping, providing a boost to the British economy in these areas. Since ideas like Political Correctness simply didn't exist at that time, you can be certain that the foreigners would be treated with suspicion, held in "ghettos" and shamelessly taken advantage of, and of course the foreigners would be organizing themselves with gangs and local associations to fight back.
The British also had a secret service which was almost 200 years old by that time (Sir Francis Walsingham having founded the modern British secret service in Elizabeth's time), so these areas would be flooded by British operatives and running agents to ensure there would be no trouble.
Since the upper echelons of British society would be driven by both shame at losing, fear of French dominance on the continent and unrest at home, there would be a constant stoking of the fires to keep people's attention on France and build support for continuing military action. Aristocrats in particular wold be flocking to the Royal Navy in order to purchase commands of warships (frigates in particular) in the hopes of capturing French prize vessels and becoming wealthy (or recovering their commissions as a minimum). As sharing of prize money was a well established practice, the Royal Navy might also become a magnet for eager recruits seeking to gain their fortunes. A large and expanding navy would certainly provide the basis for a new British strategy for "round two".
So the British society would be energized by the appearance of large numbers of foreign exiles, certain areas of the economy would experience growth due to the influx of new labour resources and the British would be moving towards a more "Maritime" war strategy to harass the French and prepare the ground to resume the conflict on more favourable terms to the British.