Winds of up to 160mph smashed into Cuba's northern coast on Saturday hours after it was classified as a Category 5 storm.
Irma has now been downgraded to a Category 3, but is forecast to restrengthen once it moves away from Cuba,according to the US National Hurricane Centre.
Concerns are also mounting over Hurricane Jose, which is growing in strength and heading towards islands already devastated by Irma.
Florida is bracing for Irma to hit on Sunday morning. It is expected to bring massive wind and flooding damage to the fourth most populous US state.
Governor Rick Scott warned that Irma, the most powerful Atlantic Ocean hurricane in recorded history, is wider than the "entire state".
More than six million people - a quarter of the Florida's population - have been ordered to evacuate.
The Carolinas, Alabama and Georgia have also declared emergencies.
Foreign Secretary Boris Johnson said the UK was "taking swift action to respond" to the disaster after speaking to the chief minister of Anguilla, a British overseas territory that was among the first islands to be hit.
Britons in the region have been urged to follow evacuation orders, while states of emergency have been declared in Puerto Rico, Cuba and Florida - amid fears Miami could be struck directly by the hurricane.
A British naval ship has been deployed to help deal with the aftermath with 40 Royal Marines on board, as well as army engineers and equipment, as authorities struggle to bring aid to smaller islands.
‘Biggest natural catastrophe on French soil in 35 years’
Hurricane Irma has caused inflicted 1.2 billion euros (£1bn) of infrastructure damage on just two islands, France's public insurance agency has estimated.
The French overseas islands of Saint Martin and Saint Barthelemy have suffered severe damage in the storm.
The Caisse Central de Reassurance, France's public-sector reinsurer that provides coverage for natural disasters, said the amount covers damage to houses, vehicles and businesses.
It added that Hurricane Irma is "one of the biggest natural catastrophes to have occurred in France in 35 years."
More than 25,000 people in Florida are without power
Only the outer bands of Irma have hit Florida thus far, but thousands of people in Miami-Dade and Broward counties are without power, according to Florida Power and Light.
The company said on Twitter that it would work to restore power throughout the storm, whenever safe.
The latest from The Independent's Clark Mindock, who is at the Florida International University Shelter in Miami as Floridians prepare for Irma to make landfall:
Jorge Herrera has lived in Homestead, Florida for nine years, and evacuated fearing the worst.
“It makes you think about everything. It makes you think we’re nothing,” Mr Herrera said. “We’re just here, and then we’re gone.”
The damage “makes you think about what’s fair and what’s not,” he added.
Jose Soto, 17, is concerned about his home. He said that he and his mother worked hard to have enough money to buy the house they moved into just months ago. He spent his time outside of school working jobs to pitch in.
“Me and my mom busted our a** to get that house,” Mr Soto said. “Hopefully it doesn’t get destroyed because we just got it.”
Hurricane Irma has been downgraded to a Category 3 storm but is expected to restrengthen as it leaves Cuba, the National Hurricane Center reports.
The storm has winds of 125mph and is moving west, toward Key West, Florida. It is expected to hit Florida Sunday morning. Those living in the storm's path are still strongly encouraged to evacuate.
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