Wind speeds in parts of England have reached 60 mph as Storm Freya hit the south west of the UK.
Fallen trees and power lines have been reported, while the Met Office issued a warning for injury and danger to life from flying debris.
Some roads have also been closed and homes left without power.
BBC Weather said conditions would deteriorate throughout Sunday with the storm set to bring winds of up to 80mph.
The warning covers parts of Wales, south-west England, the Midlands, northern England and southern Scotland from Sunday afternoon to Monday morning.
Gusts of nearly 60mph were recorded in south-west England, with main roads partially blocked in Cornwall and Devon due to fallen trees and power lines.
In Wales, a major road has been flooded and hundreds of homes were left without power.
Strong winds swept across Scotland on Saturday night as a separate weather system moved inland.
A gust of around 70mph was recorded at South Uist, while winds of 45 to 50mph blew through Glasgow and Edinburgh.
The storm follows a week of record-breaking winter heat in the UK.
But Met Office meterologist Dean Hall said Devon and Cornwall had been the first to feel the weekend’s storm, with gusts of nearly 60mph on the west coast.
He said the wind was expected to peak at about 19:00 GMT, with speeds of about 50 to 60mph likely in the warning area.
Coastal areas, particularly in west Wales, could see gusts of 70 to 80mph.
BBC Weather’s Gemma Plumb said the storm, moving in from the south and west of the UK, was expected to push north across much of the country on Sunday.
She added: “For a time during Sunday evening and overnight there is the risk that some rain could fall as sleet or snow on the hills of southern Scotland and northern England.”
Travellers are advised to plan journeys ahead, as road, rail, air and ferry services may be affected with longer journey times and cancellations possible.
Some roads and bridges may also have to close.
The storm warning comes after a week which saw the UK break its warmest winter day record on two consecutive days, with 21.2C recorded in Kew Gardens, London, on Tuesday.
The Met Office has also provisionally announced that last month was the second sunniest February on record for the whole of the UK.
The forecaster said there were average maximum daily peaks of 10C, beating the previous record of 9.8C set in 1998.
Last February, temperatures in the UK plunged as low as -11.7C at South Farnborough, Hampshire.
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