The idea that "Britannia rules the waves" simply wasn't true until the Napoleonic Wars. While the British certainly had the upper hand they certainly didn't dominate the seas with the same impunity as they did after Trafalgar. Remember, the most crucial naval battle of the Revolutionary War at least for the US theater, Chesapeake Roads, was a British defeat strategically, though tactically indecisive. And a French army landing on Great Britain means that the Royal Navy almost definitely loses Portsmouth/Spithead, and likely the Nore and other naval bases. Reprovisioning, refitting, and repairs all become exponentially harder to coordinate on a fleetwide level, while the French can simply destroy most of the facilities if they do not want to risk their recapture. Merchant ships won't be much help as by this point there was enough technical difference between merchantmen and men of war to make it very difficult to convert a merchant fleet on the fly. Furthermore, either way, they will suffer the major economic drawback of that fleet being heavily damaged.
Now, even with this being the case, the British have the advantage of numbers and of freindly terrain in the island as a whole, but the militia really, IMO, can't be assembled in time to, say, relieve an attack on London. Thus, I imagine the British will sue for peace, with Parliament panicking and/or deciding that the costs of war outweigh the cost of making peace. Terms IMO would include some or all of the following, ordered from most to least likely, though not with any particular vigor.
1. GB recognizes the US with borders roughly akin to OTL, though maybe there is some dispute over the Ohio Valley.
2. Ireland is released as a sovereign state under a Bourbon king with the understanding that the King of Ireland may never inherit the French throne or vice versa. France in exchange formally disavows its support for the Jacobin pretenders.
3. GB returns Menorca to Spain. I find this likelier than a return of both Menorca and Gibraltar which wouldn't happen unless either the Franco-Spanish army decisively defeated a large portion of the British Militia, attacked and took London, or both.
4. GB cedes various Caribbean territories to Spain, France, and/or the UP.
5. GB returns Quebec to France
6. Something in India???