The independent Commonwealth Caribbean countries have been largely unsuccessful financially, regardless of how long they have been independent. For example, the country that has been independent for the longest time, Haiti, is the most impoverished nation in the region.

British control, as you call it, provides a solid legal and financial structure for the dependent countries. After gaining independence there were struggles to modify laws and provide for a stable structure that enables economic prosperity for the nation. The citizens of dependent nations are, in general, much better off than their independent neighbors.

Source: Commonwealth Caribbean Law and Legal Systems, Antoine.