The eye of Irma passed over Barbuda, a tiny Caribbean island of about 1,800 people, on Wednesday, destroying telecommunication systems and cell towers.
The gift came as the Foreign Office confirmed that more than half a million British nationals and holiday makers were caught in the path of the mega-storm last week.
"Just, 'Oh yeah, we went down there and did this and it's done.' Because the recovery process is not going to be done".
Blondel Cluff, Anguilla's representative to the U.S. and the European Union, told CNN that 15,000 people were now stranded on the island and dependent on humanitarian aid for their basic needs.
The EU also announced an initial aid package of $2.4 million for emergency relief.
Royal Fleet Auxiliary Mounts Bay is providing immediate assistance, including Royal Engineers and Royal Marines to fix vital services ashore.
Addressing concerns about the speed of Britain's response, Mrs May said both humanitarian workers and RFA Mounts Bay had been "prepositioned".
Defence Secretary Michael Fallon rejected the criticism, saying the United Kingdom had responded "very quickly", with one ship helping in Anguilla since September 7.
The storm destroyed almost all buildings on the island of Barbuda on Wednesday, leaving it "barely habitable", and killing a two-year-old child as a family tried to escape.
Irma was downgraded to a tropical storm early on Monday, after inflicting record flooding and deadly devastation in Florida and on several Caribbean islands.
On his blog, meanwhile, dad Richard - who spent the storm in his wine cellar while his island was devastated - said he and his team have been doing "everything we can to help the community" in the BVI.
"We had the storm hit, we watched the storm rip the roof off our hotel room, we sought shelter in different places during the back end of the storm", Conger said.
She said the needs were "unprecedented" but admitted getting kit and people into the region had been challenging. "That's the problem, everyone has their own problems at the moment", Cluff said.