Born in Stoneleigh, Warwickshire, Drax migrated to the English colony of Barbados and acquired ownership of several sugar plantations and slaves.
[4]: 14–15 Drax and his companions lived in a cave for a time, searching for provisions, hunting turtles and hogs and also clearing land for the planting of tobacco, which soon became the staple crop of the island.
[5][4]: 14–15 Drax later claimed he had arrived with a stock of no more than £300, and that he intended to stay on the island until he had parlayed that initial investment into a landed fortune worth £10,000 a year back home.
A slump in tobacco prices created considerable economic difficulties in England's fledgling colonies in the Caribbean in the late 1630s, and white colonists began to turn to other crops.
Barbados quickly became a major supplier for Europe, and by the mid-1650s, sugar production had largely supplanted tobacco and all other crops as the dominant economic activity of the island.
Although there were enslaved Africans in Barbados before that time, it was only after 1640, and frequently in tandem with the cultivation of sugar, that slaves began to supplant indentured servitude as the main workforce.
When a royalist faction seized control of Barbados in 1650, James and William Drax were exiled from the island, along with other prominent parliamentarians.
In 1651, Drax sailed in the fleet designed to re-conquer Barbados, and he was part of the delegation that went ashore to negotiate the surrender of the island.
It is thought that he and his brother ordered Drax Hall, a seventeenth-century manor house in St George parish, Barbados, to be constructed during the 1650s.