Was slavery used in Britain at the height of its use in the US?

Slavery had been banned for decades in the British Empire by the time of the Civil War, and been banned in Britain itself for nearly 100 years (practically; actually, slavery was banned in Britain many centuries before, but British slaveowners occasionally brought slaves to Britain as domestic servants. They couldn't buy or sell them in Britain, so there were only 10000 or so. But in 1774 a legal case established that, as no law had been passed making it legal, it was not legal to have slaves in Britain, and all slaves were automatically freed; this was about 10000 domestic servants).

In the late 18th century, a religiously-motivated Abolition movement developed, comprising mostly Quakers and Evangelicals (I should probably note that 18th-19th century British Evangelicals are not very similar to the 21st century American Evangelicals you may think of today). Led by William Wilberforce, they pressured the government and campaigned to sway public opinion against slavery, eventually successfully. (There were also economic and geopolitical reasons; Britain was becoming less reliant on slave labour for its wealth, due to the flourishing industrial revolution. And being against slavery was a useful way of showing British moral superiority over the Dutch, French, etc)

The Slave Trade Act 1807 made it illegal to buy and sell slaves in the British Empire, but didn't actually free slaves (as I said, in the UK itself, the smallish number of slaves had already been freed, but there were still many, many slaves in Jamaica and other colonies). Britain then created an anti-slavery division of ships which patrolled West Africa seizing slave ships (regardless of their country of origin) and freeing slaves (though this did mean, sadly, that sometimes slavers would just throw all their slaves into the sea to get rid of the evidence). This is why most slaves bought by Americans in the mid-19th century were from other American slave owners, not slave traders bringing them from Africa: there was a good chance slave traders would be attacked by British ships (though of course, it did still happen).

The Anti-Slavery society continued to campaign to free those still in slavery. At Christmas 1831, a Baptist minister in Jamaica organised a peaceful march of slaves demanding freedom. This became a strike, which led to a brutal suppression by British soldiers. This further turned British public opinion against slavery on moral grounds. So in 1833 the Slavery Abolition Act was passed, which freed slaves (though in stages: it wasn't until 1843 that they were all actually freed) and paid compensation to slave owners (£20m in total).

So, by the time of the civil war, there'd been no slaves in the British Empire for about 20 years, and no slaves in Britain for about 90.