The Met Office has issued a yellow warning for severe gales for west Wales and south west England from 3pm on Sunday through to 9am on Monday.
Storm Atiyah, named by the Irish meteorological service Met Eireann, is expected to move from west to east during this period.
The first named storm of the season could bring winds of 50-60 mph inland and up to 70 mph on the coast, the Met Office said.
The weather is turning more unsettled tonight, and there's more wet and windy weather on the way into next week.
Here are the details 👇 pic.twitter.com/QagjJQ1M95— Met Office (@metoffice)December 7, 2019
Areas outside the warning area could still see winds of between 40 and 50 mph.
Widespread heavy rain will sweep across the country while snow is set to fall on higher grounds in northern England, Scotland and Wales, forecasters said.
Sophie Yeomans, a Met Office meteorologist, warned that strong winds on Sunday could trigger delays on the roads and rail disruption.
She urged the public to "take care around the coast" due to large swells possibly being whipped up.
Ms Yeomans added: "Christmas markets with loose items, loose structures, it's one of those to check is everything secure - your Christmas lights, inflatable Santas."
"Make sure that you're aware of those wind warnings," she added.
She explained that the windy conditions would be worse on the Irish coast.
The Met Office previously said that strong winds are also expected for western parts of Northern Ireland and Scotland, with gusts of up to 57mph overnight.
The unsettled weather is expected to move to the east coast of north England and Scotland in the early hours of Monday morning with gusts up to 55mph.
Ms Yeomans warned residents along the east coast of England to be wary of large waves on Monday.
Looking ahead, she said conditions on Monday would be dry in general, with the odd shower in places, but still cold and windy.
While it was too early to be certain, she explained Tuesday was expected to usher in another wet and windy spell mid-week.
Meanwhile, Met Office spokesman Steven Keates said there will be snow on higher grounds all the way through until Thursday.
"We are not collecting widespread snow in populated areas and it will be nothing unusual for this time of year," he said.