The question this rises is - will Lincoln think his hand is so good now that he overplays it and ruins the chances to get a separate peace with acceptable terms for both parties, or if he manages to strike while the iron is hot while making concessions which Her Majesty's Government will find acceptable.
There have been many comments that the USA is unwilling to cede land belonging to the original 13 colonies, but looking at maps of Maine, there's little to no settlement in the Appalachians. If the border were moved to the Allagash river, then Canada would control the spring of the St John river (mostly in New Brunswick) and there would be a mountainous secure buffer for the northern branch of the
Grand Trunk at it's closest approach to the US border. This might be a sufficient concession for British interests, without the USA losing any settlements worth mentioning.
Add to that accepting British claims in the Puget Sound area and that might be enough territorial concessions.
Lincoln does have an opportunity here. Lifting the Siege of Washington is both a big morale booster and propaganda hit. A very astute observer might say that "even with the aid of the Royal Navy the Confederacy could not take Washington" which may sour some opinions. However, he has to act fast, and Farragut's victory is also a good propaganda moment since it might be able to drive home that the war is still costly for Britain too. With most of Britain's war aims being accomplished, Canada not in danger of being bisected, and the Union not a real threat to Britain's North American and Caribbean possessions, maybe he
can entice Britain out of the war with some juicy concessions?
The British very much have an idea of the ideal concessions they'd like to take. Not all of them are territorial either. However, the War Cabinet is very hawkish at the moment, and they have some firm opinions on what should be done.
Realistically, I see any British Empire that went to war with the US over a Trent Affair being very very committed to getting something out of the war. They would, unless totally humiliated in the field somehow, fight on with what they have in order to maintain some pretense of national prestige. Too many modern people tend to forget that in this era war is not just looking at a balance sheet, but thoughts of national honor and a feeling that you have to maintain face. Even if Canada was lost, the British felt they could maintain the blockade almost indefinitely, and eventually push the Union to the negotiating table through economic means. There isn't really a scenario where the Union can deliver any combination of blows that
materially effects Britain enough that they have to sign an extremely disadvantageous peace.
In
Wrapped in Flames, Britain probably could have been convinced to sign what amounts to a "White Peace" with financial reparations only in September 1862, when the Palmerston government TTL assumed their strategic calculus would force Lincoln to the table to accept their original December Ultimatum. However, with how the war went, the Lincoln government still felt they could obtain better terms than the original British demands and fought on. By September 1863 however, even with British reversals in the field, there's no chance Britain will sign anything resembling a peace under the terms offered in December 1861 now that the blockade is still biting and there is a less than zero chance the Union can seriously threaten Canada again.