The South West could be hit by winds of up to 75mph (121km/h) later as Storm Evert hits the UK. (BBC NEWS)
The Met Office has issued an amber warning for severe gales across the region, strong enough to damage buildings and disrupt travel.
The storm is also expected to hit the south Wales coast from Monmouthshire in the east to Pembrokeshire in the west.
BBC meteorologist David Braine said it was "exceptional" for this time of year.
Evert is the fourth storm to be named by the Met Office since October last year.
Strong winds and heavy rains are expected to first hit the Isles of Scilly on Thursday evening, before spreading over to Cornwall in the early hours of Friday, the Met Office said.
The gustiest of winds, at 75mph (121km/h), could be expected in the county's "most exposed coastal spots", it added.
A yellow warning for strong winds has also been issued for parts of Devon and Wales.
It means the South West is likely to see fallen trees, damaged buildings, power cuts and travel disruption from Thursday, the Met Office warned.
George Holtby at the Bedruthan Steps Campsite is moving guests to a field that is better protected from the wind.
"It's an exposed site, so we're advising people to strap everything down and batten down the hatches," he said.
Sarah Weeks, of cliff-top glamping site Seaview Tipis at Bredruthan Steps in north Cornwall, is urging guests to "pack up and go tonight because it's the safest thing".
Guests are being offered compensation or vouchers for later visits.
Highways England is warning drivers to take extra care as the storm moves in.
"In high winds, there's a particular risk to lorries, caravans and motorbikes so we'd advise drivers of these vehicles to slow down," said South West emergency planning officer Gareth Price.
"Drivers of other vehicles should be aware of sudden gusts of wind which can affect handling and braking, and give high-sided vehicles, caravans, and motorbikes plenty of space."
The Met Office has issued an amber warning for severe gales across the region, strong enough to damage buildings and disrupt travel.
The storm is also expected to hit the south Wales coast from Monmouthshire in the east to Pembrokeshire in the west.
BBC meteorologist David Braine said it was "exceptional" for this time of year.
Evert is the fourth storm to be named by the Met Office since October last year.
Strong winds and heavy rains are expected to first hit the Isles of Scilly on Thursday evening, before spreading over to Cornwall in the early hours of Friday, the Met Office said.
The gustiest of winds, at 75mph (121km/h), could be expected in the county's "most exposed coastal spots", it added.
A yellow warning for strong winds has also been issued for parts of Devon and Wales.
It means the South West is likely to see fallen trees, damaged buildings, power cuts and travel disruption from Thursday, the Met Office warned.
George Holtby at the Bedruthan Steps Campsite is moving guests to a field that is better protected from the wind.
"It's an exposed site, so we're advising people to strap everything down and batten down the hatches," he said.
Sarah Weeks, of cliff-top glamping site Seaview Tipis at Bredruthan Steps in north Cornwall, is urging guests to "pack up and go tonight because it's the safest thing".
Guests are being offered compensation or vouchers for later visits.
Highways England is warning drivers to take extra care as the storm moves in.
"In high winds, there's a particular risk to lorries, caravans and motorbikes so we'd advise drivers of these vehicles to slow down," said South West emergency planning officer Gareth Price.
"Drivers of other vehicles should be aware of sudden gusts of wind which can affect handling and braking, and give high-sided vehicles, caravans, and motorbikes plenty of space."