Britain had a strong anti slavery faction, which had contributed to ending slavery in the Empire. Lets think for a moment that group being a bit more active in 1861 & having larger influence in the government.
How much more active do you want the anti-slavery movement to be? The Confederate ambassador James Mason concluded after his time in Britain that "In my conversations with English gentlemen, I have found it was in vain to combat their
sentiment. The so-called anti-slavery feeling seems to have become with them a sentiment akin to patriotism." Richard Huzzey recently came to a similar conclusion: "anti-slavery became an article of faith in Victorian Britain... the wrongness of slave-holding and slave trading had become an unassailable truth, unacceptable to question publicly" (
Freedom Burning: Anti-Slavery and Empire in Britain, 2012, p.17). The idea that anti-slavery was in decline is a myth, largely created to explain away the fact that British found the Union's commitment to the anti-slavery cause too half-hearted to sympathise with.
The Republicans and Abolitionists sense the opportunity and have built connections & influence across the Atlantic.
How do they accomplish this without alienating the people they're trying desperately to keep on side: slave-owners in the Border states, and slave-owning Southern Unionists? As I described in
this post, key abolitionists do attempt to build British sympathy on the grounds of shared anti-slavery interest. However, these attempts are stymied by the utter lack of any tangible evidence that the Union opposes slavery. It's simply impossible to lie to a country about how anti-slavery you actually are when they can- and do- read your own newspapers.