The first hurricane of the Atlantic storm season skirted past the Cayman Islands today and raced on towards Mexico's Caribbean coast after battering Jamaica with winds of up to 150 mph overnight.

With the storm still gaining in intensity as it loops westwards across the Caribbean, it had looked like disaster could be looming for the low-lying British tax haven. But in the event the eye of the storm passed some 100 miles south of the islands and officials said that the strongest wind gusts were measured at just 57mph (92kph).

The Cayman Islands government announced that the territory had "been spared the brunt of Hurricane Dean".

The storm has killed at least eight people as it has moved across the Caribbean, although Jamaica also managed to avoid its most deadly effects as the storm barrelled along the island's southern coast last night.

The Jamaican capital, Kingston, was hit by hurricane-force winds which downed power lines, ripped off roofs and blocked roads with debris before spiralling off into the Caribbean in the early hours. But there were no reported deaths and thousands of holidaymakers – including many Britons who took refuge in the most solid buildings – emerged unscathed.

"I think the feeling around here appears to be more of relief than anything else," said Richard Susskind, a Times law columnist who spent the night holed up with his family in a conference centre in a resort near Montego Bay.

"Dawn is beginning to break and although the roads are completely covered in debris from the trees, there is no sign of any radical damage."

Meanwhile, the Foreign Office updated its travel advice for the region and issued a warning to British tourists not to go to the Central American country of Belize, which lies under Mexico's Yucatan Peninsula and is now firmly in Dean's sights.

American forecasters said that the storm was projected to become a potentially catastrophic Category Five storm, packing sustained winds of 160mph, as it passes across the Caribbean into the Gulf of Mexico. It is expected to hit the Yucatan peninsula, a tourist haven, and Belize tomorrow.

"Fluctuations in intensity are common in major hurricanes and are possible in during the next 24 hours," the US National Hurricane Centre reported today. "Dean has the potential to become a Category Five hurricane in the northwestern Caribbean sea on Monday - like Gilbert in 1988 and Wilma in 2005."

That reference to the two most intense storms ever recorded in the Atlantic basin – which between them killed more than 400 people – was guaranteed to strike fear across the region.

Mexico was evacuating some 90,000 tourists from Cancun and other islands of the "Mayan Riviera," as well as some 13,000 workers on more than 140 of its oil platforms in the Gulf of Mexico.

Times Recommends

• Rio Tinto four held as China prepares case
• Diplomats must keep heads down and trousers up
• When in Rome should one make like Berlusconi?