Foreign Secretary Boris Johnson has praised the response of the community in Anguilla after landing on the island to witness first-hand the devastation unleashed by Hurricane Irma.
Britain has sent more than 700 troops and 50 police officers to the British Virgin Islands after Irma swept through last week.
"We have maintained and kept law and order on the BVI which at one point could have dramatically threatened the already unfortunate plight of those that have been hit by the hurricane".
British overseas territories, including Anguilla, Turks and Caicos and the British Virgin Islands, are self-governing but rely on the United Kingdom government for protection against natural disasters.
On Monday, Mr Johnson said further support would soon be made available on top of the £32m already pledged to the relief fund.
The UK has provided more than 40 tonnes of aid including 2,608 shelter kits and 2,304 solar lanterns.
"We had RFA Mounts Bay in position in the region before the hurricane struck - it would have been totally absurd to bring troops in or bring heavy aircraft during the storm itself".
Image France has sent hundreds of troops and emergency workers to St Martin
HMS Ocean left Gibraltar on Tuesday night stacked with more than 200 pallets of aid including timber, buckets, bottled water, food, baby milk, bedding and clothing. "It will go up to 1,250 in the course of the next few days".
But shadow foreign secretary Emily Thornberry said the British government's response was "too little and too late" and talking about potential evacuation a week on from the disaster was "alarming".
He said consular staff were in the region trying to get in touch with Britons who were on other Caribbean islands, not under British responsibility.
The Royal Navy's fleet flagship has set sail for the Caribbean loaded with long-term emergency supplies for British territories devastated by the storm.
Duncan said a total of nine people died in British Caribbean territories - five in the BVI and four in Anguilla. Expected to require extensive humanitarian assistance.
Branson posted photos on Twitter and Instagram showing the damage wrought on his island and wrote in a blog that climate change should be taken more seriously by governments.
Warnings of unsafe storm surges remained in effect through vast swaths of peninsular Florida, where more than six million people had been ordered to flee Irma in one of the biggest evacuations in USA history.
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We urge you to take decisive actions to stop the violence against innocent civilians and bring permanent peace in Rakhine state. Others, which were "very decomposed", were thought to be from other boats that had capsized earlier, he said.