He told MPs there had been a “serious threat of the complete breakdown of law and order”.
Royal Marines were sent in on Friday to “protect the Governor”, he added.
Foreign Secretary Boris Johnson is on his way to the Caribbean, amid criticism that the UK’s response has been “too slow”.
More than 500,000 British nationals have been in the path of Hurricane Irma, Sir Alan said, adding that five people are now known to have died in the British Virgin Islands and four in Anguilla.
Addressing the House of Commons, Sir Alan said there were 997 troops in the region and 47 police officers had been sent to the British Virgin Islands (BVI).
“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.”
He added that dealing with the security breach “was what ministers and the ministry of defence was for”.
British overseas territories, including Anguilla, Turks and Caicos and the British Virgin Islands, are self-governing but rely on the UK government for protection against natural disasters.
On Monday, Boris Johnson said further support would be announced within days on top of the £32m relief fund already made available.
The UK has provided more than 40 tonnes of aid so far including 2,608 shelter kits and 2,304 solar lanterns.
RFA Mounts Bay, which was pre-positioned in the Caribbean ahead of hurricane season, started helping in Anguilla on 7 September.
Meanwhile, a second ship HMS Ocean has been deployed to provide aid and assist the reconstruction effort.
Some 250 military personnel will be sent to the Caribbean “in the next few days” bringing the total to around 1,250.
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”.