As an aside you'd be absolutely shocked how few of the British higher ups gave a damn about slavery in this case.
I think you'd be shocked how many did. When Lincoln came to power, he announced he had no intention to act against slavery in order to avert a war. While Palmerston was in power, he was prepared to risk war with- among others- Portugal, Brazil, Spain and the US in order to combat the slave trade. In 1860 he explains to Gladstone that he has "two great objects always before him": one was the defence of England, the other was the abolition of the slave trade.
But, you may say, this only applies to the slave
trade, not to slavery itself. That seems a little unfair, given that Palmerston never differentiated between the two- to him, the trade was "the root which gives life and spirit and stability to the condition of slavery... lay your axe to the root, cut off the supply of nourishment, and the tree will sicken and die, and you will no longer find difficulty in bringing it to the ground". If we argue that Palmerston is not anti-slavery because he focuses on the trade, that leaves Lincoln's focus on the territories on extremely shaky ground. Not to mention the fact that Palmerston was already voting for abolition of slavery in Britain at around the time that Lincoln was starting to aspire to membership of the Illinois legislature.
Contemporary observers were clear on Palmerston's hatred for slavery. CP Villiers wrote to John Bright in January 1862 that his detestation for it would mitigate against him dealing with the Confederacy. Motley wrote the same to Seward in October 1862. The fact that his fundamental motivating political principle seems to disappear when dealing with this topic is a fault in the historiography and not in Palmerston himself.
despite the words of many politicians, most people of the time knew this war was about slavery...The British knew this too.
The British, or at least the majority of them, knew that the South had left the Union because of slavery. What they also knew was that Lincoln had disclaimed any intention to interfere with slavery, that Congress had passed a resolution in July 1861 saying the war was about preserving the Union not freeing the slaves, that there were slave-owning states still in the Union, one of which- Missouri- had attempted in late 1860 to have an escaped slave extradited from Canada to be burned alive, that Seward had requested foreign powers to return escaped slaves to their owners, that Lincoln had countermanded Fremont's own emancipation measures, that free blacks in the Northern States suffered levels of racial discrimination which even the British considered excessive, that the Emancipation Proclamation didn't touch slaves when their masters were loyal...
What the British knew was that if the South had decided that slavery could be secured within the Union and offered to lay down their arms and returning to the Union in return for it being secured, they were likely to get their way. The fact that in 1864 Lincoln drafted a private letter saying "if Jefferson Davis wishes to know what I would do if he were to offer peace and reunion, saying nothing about slavery, let him try me" strongly suggests that what they knew was right.
There are two areas that they're perhaps confused on. One is the fact that the South refuse to take an apparently easy avenue to secure slavery: this leads many to the incorrect conclusion that the South wants independence rather than the correct conclusion that they consider independence the best way of securing slavery. The second is that they are over-optimistic about the likelihood of slavery ending in the event of Southern independence: however, this is entirely understandable not just in the light of contemporary beliefs about providentialism and progress, but also when you consider that the British could expect to have the North pushing for abolition alongside them instead of helping to shore it up as they have done previously. What they weren't confused about, and what even the strongest Union partisan will concede, is that there was a serious risk that the restoration of the Union could have made slavery more, not less, secure than before.
Incidentally, the answer to this question:
Why didn't Britain intervene in the American Civil War?
can be found by taking a sheet of paper, making a list of all the civil wars which took place between 1815 and 1914, and then highlighting all the ones in which Britain intervened. Joining in a civil war took place only under absolutely exceptional circumstances: despite the amount of times it comes up on this boards, the closest that Britain
actually came to intervening in the American Civil War was scheduling a cabinet meeting to discuss the propriety of raising the question with other European governments as to whether they should come together and make a non-binding offer of mediation. That's it, unless you count all the times that someone raised the question of intervention in
Parliament and was shot down by a member of the government.