The British Empire outlawed slavery BEFORE the United States did. I don't know where OP is going with this. Western Civilization (led by the UK) deserves immense credit for the global effort to eradicate slavery. Other civilizations didn't want to end slavery -- some still practice it.
American legislatures were attempting to get rid of slavery as early as 1765, Massachusetts. Governor Hutchinson vetoed it. They vetoed several anti-slavery laws.
Is that America’s fault or Britain’s fault?