The primary reason that so many slaves came to the West Indies, Brazil, and America, was that they were taken from their African origins and transported to these other countries, by the running and usage of ships specifically made for that very purpose. In both America as well as Great Britain, there was a moral outrage that certain human beings were treated as chattel, forcefully taken from their homeland, and bought, treated, and sold as if they were cattle. Although many saw this injustice and desired strongly to outlaw slavery, the practicalities of that day and age dictated that this was politically impossible, so instead, alternatively, they were able to enact in 1807 laws that abolished the slave trade (the United States law to this effect was passed in 1807, but came into effect on January 1, 1808). The passage of this significant piece of legislature seem to signify that since the territories controlled by the British Empire as well as the United States itself, would no longer be legally importing slaves that this would over a period of time, reduce significantly slave populations, which basically became true for the British Empire but not for America. The most meaningful reason why American slave populations actually rose each decade after the slave trade was abolished, is that America for the most part, did not have the same sorts of diseases such as yellow fever and malaria that decimated so many slaves in the West Indies, as well as the fact that despite the illegality of the slave trade, slaves were still imported in significant numbers into America.
Though both America and Great Britain had navies, Great Britain's navy was the strongest and the most powerful navy in the world, in which, Great Britain devoted resources and time to eradicating illegal slave running from Africa to the territories that were part of the British empire and were fairly successful in so doing. America, on the other hand, devoted minimal energies to interdict slave trafficking, in addition to the fact, that rather than importing slaves through ports it had previously used while the slave trade was legal, had many of their newly trafficked slaves imported through Texas and Florida, of which neither became a State of the union, until 1845. So that, while the eliminating of slave trafficking in the British empire led to its logical conclusion which was the eradication of slavery, itself, by British Parliament in 1833; regrettably, on the other hand, in America, the slave population increased from as reported in the United States census at 1,191,362 slaves in 1810 to an incredible 3,953,761 slaves in 1860, this during a time period when the importation of slaves into America was illegal! No doubt, part of this increase could be attributed to the slave population increasing through reproduction, but a significant amount of this increased number came from the illegal slave importation, so that, when the slave trade act in America was passed in 1807, the impression that by so doing, that slavery would over the years, gradually fade away and thereby become less and less of an economic necessity or need, was found to be wholly false, instead, the issue became such a conflict and inimical to what America represents, that a great civil war was fought, in order to resolve this issue which had torn this country asunder.
Laws, in general, are only as good as the equal application of that law as well as the equal enforcement of such. In Great Britain, the abolishment of the slave trade did indeed lead to the abolishment of slavery, of which, this was done without revolution and a minimum of bloodshed. In America, the abolishment of the slave trade, led to a certain segment of the population ignoring such, for they knew that they would suffer not, until such time, when a President was elected that they feared would call them to account, in which, this led to the fateful steps that abolished slavery in America, but not until thousands upon thousands died in this just but bloody cause.