I'll start out with this, and repeat after me:
The Civil War was not about Slavery. It was about states rights.
The state right that was being disputed was Slavery, but that's not what the war was about.
Lincoln didn't make it about Slavery until around the time of Emancipation Proclamation, when it had become clear they needed something stronger to fight about beyond "Keeping the union together".
The British had started the Anti-slavery squadrons because it aligned with their foreign objectives. The Morality of it was an excuse. Its estimate that 11 million people entered the slave markets of the Americas; only 300,000 entered the North American slave market. The rest went to Plantations in Brazil, Carribean, and Gran Columbia (Columbia, Panama, And Venezuela) - at the time Portuguese and Spanish (and spanish-aligned post independence) colonies (the Spics).
The British Colonies/the US imported so few because, putting it bluntly, they put a breeding program in place to home-grown the population. In Brazil especially, slaves were treated as expendable. The British anti-slavery efforts didn't affect the Confederacy much to at all.
Spain was the last European power to traffic in african slaves, and by disrupting that highly profitable enterprise, Britain was making sure Spain was weakened.
now, on to the Darkies & Dune coons.
At the time, the British were backing regiemes that ran partly or wholly on slavery, but they had moved away from the practice for two reasons:
1) Britain didn't directly benefit from slave labor. They had the Irish to abuse & exploit.
2) It gave them a "moral imperitive" to invade places where slavery existed (literally everywhere but Europe).
So fighting slavery gave the British an excuse to be fucking around in north-west africa. It also gave the a reason to push their sphere of influence in East Africa, and start putting pressure on the Ottomans, the sick man of Europe.
But the British were very tolerant of worker abuse in their empire AS LONG AS YOU DIDN'T CALL IT SLAVERY.
If given a strong enough incentive, the British media would have spun it to justify intervention.