The highest alert level means there is danger to life from flying debris, while power cuts are likely.
A severe weather warning has been upgraded to red – the highest level – for parts of south-west England and south Wales on Friday, meaning there is a danger to life from flying debris.
The Met Office warned Storm Eunice could bring gusts of up to 90mph, causing significant disruption.
Damage to homes, train cancellations and power cuts are also likely.
A lower amber warning for wind remains in place for the rest of Wales and most of England as far north as Manchester.
The government is holding an emergency Cobra meeting to discuss the response to the incoming storm.
There are concerns that Storm Eunice could bring coastal flooding to the west, south-west and south coast of England.
The River Severn is also an area of concern.
A government source told the BBC that a storm surge could coincide with high spring tides.
The source said they were “well-prepared” with more than 250 high volume pumps and 6,000 trained staff able to be deployed, adding they were not taking the threat posed by Eunice “lightly”.
The red warning is in place from 07:00 GMT until 12:00 on Friday.
The Met Office said extremely strong winds would develop over south-west England and south Wales early on Friday, with widespread inland gusts of 70-80mph and up to 90mph near some coasts.
Conditions would be dangerous on beaches and seafronts, it said.
The winds are expected to ease from the west during the late morning.
A Rare Red Weather Warning ⚠️ has been issued as #StormEunice is expected to bring extremely strong #winds and continued disruption for much of the UK on Friday. Read our latest news release for more information 👇🏼📰— Met Office (@metoffice)
Meanwhile a red weather warning has also been issued for the south-west of Ireland.
The Met Eireann storm warning for Counties Kerry and Cork is in place from 03:00 until 08:00 on Friday.