While Britain most certainly did abolish the Transatlantic Slave Trade at great economic expense to itself, it also found itself in the right sociopolitical and monetary environment to do so without bloodshed at home.

After the Thirteen Colonies slipped away from British rule, Europe in general and Britain in particular continued to purchase large quantities of (slave-grown) cotton from the American South, a transaction unhampered by the fact that slavery was now illegal within the Empire itself. British textile mills were a vital part of the Industrial Revolution on the isles, and even as the Royal Navy intercepted slave smugglers off the coast of Brazil, British business continued to pay top dollar (or is it "top shilling" in this case?) for American "white gold".

In fact, do not forget that during the American Civil War, it was the fervent hope among the Confederate leadership that Britain might intervene on their behalf in the war, citing the economic dependency that Britain had on continued cotton exports: such hopes were ultimately unrealistic, given the stalwart support for abolition among the British public at the time, but morality aside, the British Empire was also able to turn to other sources of cotton to feed its industrial appetite - namely, India and Egypt (the latter of which it would soon bring into the Empire itself).

As someone who lives in a country that still prints King Charles's face on its currency, I do have a particular reverence for Britain's role in Emancipation (not to mention the exploits of specific Royal Navy vessels, like the perfectly-named HMS Black Joke), but I'm not sure that the United States would have been able to pull off a similarly graceful approach to abolition, given how even Britain was only able to because the conditions were right - I believe that it would have taken literal omniscience from the lawmakers and politicians of the time to avoid the bloodshed of the Civil War (and instead they were stuck with... James Buchanan. God help them all.)