The USCG and BVI do cooperate on drug interdiction (and I think human smuggling). USCG has over 2 dozen counterdrug bilateral agreements and operational procedures with partner nations including the UK and many Latin American, South American and Caribbean countries. Quoting from a USCG annual report "These agreements enable the Coast Guard to: board suspect vessels, facilitate interdictions in underpatrolled territorial waters of partner nations, deter illicit activity in the littoral regions, and coordinate interdiction and apprehension operations in the Western Hemisphere Transit Zone."

This story describes a USG cutter seizing 1700 kg of cocaine tossed off a go-fast boat near Anegada.
https://www.bvibeacon.com/tag/drug-bust/

This story describes USCG contacting BVI police for permission to follow a suspected drug smuggler from US to BVI waters. https://www.284media.com/local/2021...s-on-the-run-says-commissioner-matthews/