No BA flights will take off from Heathrow Airport to Miami on Saturday (September 9) and Sunday (September 10), with only two of its four departures operated on Friday (September 8).
In addition, all the airlines flights between London Gatwick and Orlando and Tampa will no longer depart on Sunday (September 10).
Flights from Heathrow to the Grand Cayman via Nassau will be affected too, operating direct to Grand Cayman only.
The storm has wreaked devastation on several Caribbean islands, and Miami is bracing itself with evacuations under way.
While the majority of flights continue to operate to and from the Caribbean and Florida, the situation remains under review.
BA is warning customers due to travel to any of these destinations that their plans will be affected in the coming days.
BA said on its website that it will continue to update its information page for Monday's services as more details from the airport authorities emerge.
Passengers are advised to check with their airline or to re-book.
Virgin Atlantic has said its on its website flights to and from Florida are "severely disrupted," after officials declared a state of emergency.
Services to Orlando and Miami are restricted until Monday (September 11).
The advice to customers on flights to and from Florida or the Caribbean is to check their flight status before going to the airport.
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