Britain: USA would essentially be asking for peace on the basis of status quo ante bellum as soon as war broke out. Lincoln really didn't want war with Britain, and Britain really didn't want war with the USA. (Britain believed that the USA was forcing them into it). While it's possible for the two sides to blunder into war if there's a lot of mistakes from everyone, there will be considerable pressure on both sides to end the war as soon as possible. I'd expect any realistic Trent War to be a fizzer.
CSA: Would probably need the CSA to find a way to advance to New York City, or at least Philadelphia. (In other words, not happening.) Or a long war leading to a peace of exhaustion, but that requires the CSA to do the equivalent of rolling a lot of 6s even to survive.