Cayman, BVI and Bermuda are only nominally under the UK flag. Their economies are heavily based on off shore finance, a sector which the UK govt is determined to destroy.
If the UK gov't had its way these islands would be all poor because there would be no off shore sector. In addition there have been quite a few allegations of extreme corruption at least as bad as one would find in the independent nations.
The UK ignores them except when someone in London gets a bee in their bonnet that UK is about to collapse because these islands are allowing British tycoons to get away without paying income taxes to the UK gov't.
The Bahamas is the richest independent nation as it is also a tax haven. That explains their wealth more than any UK involvement. Poverty was rampant and class oppression extreme when the Union Jack ruled the Caribbean skies. Some might have forgotten that!