The big income maker that has fueled the government is the corporate domicile formation in the bvi associated with their opaque banking structure. Though there has been some reported cracks in the system due to international pressure it remains a goto for wealthy of the world of all stripes.

British takeover would likely involve quick changes in transparency and regulation. While it should be argued that's a great policy for the world at large , it will devastate the banking industry and the largest source of income, hurting the people that corrupt government officials have been cheating. Those corporate entities would move to the Caymens,Bahamas etc along with the associated fees .

I would imagine besides many politicians not wanting to lose their power, there are some who know the impact this would have and something less than a total British take over might preserve a good deal of the revenue.

Will be hard to weed out the corruption without a takeover one would think. However I really dread seeing a much higher level of poverty hit those islands.