The British eventually turned to African slaves because they were more plentiful and easier to keep as slaves than any other group of people that was available to the British in the Americas.
In thinking about why the British turned to Africans, let us think about what their other options were. In the Caribbean, their only other option (there being very few, if any, natives by the time the British got there) was white workers, either free or indentured servants. In addition to these options, British in North America could possibly have used Native Americans, again either as paid or slave labor.
Africans were “better” than any of these options. Indentured servants became less plentiful as time went by. Fewer British people were willing to subject themselves to that particular system. In addition, indentured servants were English people who had rights of various sorts and expected those rights to be respected. Free laborers had little interest in plantation work because it was too hard and because they had better options, such as finding their own land to work. Native Americans were not ideal because they could very easily run away. They were also not versed in the ways of large-scale agriculture.
African slaves were “better” in all of these ways. They could be gotten in large numbers and had no choice but to come. They had no rights and expected no rights. They could not easily run away because they were conspicuous due to their skin color.
For these reasons, the British ended up turning to African slaves to fill their labor needs.