In OTL the Union navy stopped, boarded and captured two Confederate ambassadors on the British vessel the Trent. Lincoln was able to successfully find a diplomatic solution to the crisis, but what if Great Britain was less receptive to diplomacy and war broke out between GB and the Union, thus giving the CSA legitimacy?
My opinion is that the Royal Navy would break the blockade of the South thus allowing the Confederate States access to international trade. GB would send a small army South from Canada but I suspect that Union forces would successfully defeat any British invasion. With British recognition, Napoleon III might be willing to officially recognize Confederate independence, if the CSA helps with the subjugation of Mexico. Great Britain might force the Union and Confederate leaders to negotiate peace in 1863.