Winds of up to 80mph could batter parts of the UK as the second storm strong enough to be given a name sweeps in this week.
The Met Office said Storm Barney is set to bring gusts of up to 70mph inland and potentially 80mph along exposed coasts, though the North East looks like it will escape the worst.
Wales and through to the Bristol Channel will be particularly badly effected on Tuesday.
A yellow "be aware" warning for strong winds has been issued for parts of Wales, southern, central and eastern England for Tuesday afternoon and into the evening, as a series of low pressure systems move in from the Atlantic bringing unsettled weather.
There is also a weather warning for rain in the next few days centred on the north west of England and Wales, coming hard on the heels of torrential rain which saw rivers burst their banks and localised flooding affecting roads, farmland and train services.
The Met Office is warning that given the already saturated conditions, communities could see more floods from standing water or swollen rivers that could lead to travel disruption.
Storm Barney is the second storm to be named under the "name our storms" project by the Met Office and Met Eireann, which asked the public to suggest names.
Last week, Storm Abigail left more than 20,000 homes without power and schools closed in Shetland and the Western Isles as it swept across Britain.
The Highlands and Islands were worst hit by gusts of 84mph, while the rest of the UK experienced thundery showers as a result of Britain's first named storm.
Meanwhile, north-west Scotland is facing severe gales on Monday, with a weather warning forecasting gusts of 65-75mph.
The Met Office said the strongest winds will initially develop across the Western Isles and north-west coast before extending into the Northern Isles during the evening, before they quickly ease on Tuesday.
There is due to be a change in the weather at the end of the week with colder air spreading from the north, bringing wintry showers to the northern UK, particularly over the hills.
Despite the threat of more bad weather, the Environment Agency said the flood risk across northern England was receding - although river levels will remain high in the week ahead.
In particular, the River Ouse in North Yorkshire and York will remain high until Thursday, where there could be further localised flooding, the agency said.
Elsewhere, many flood warnings for rivers have been removed, although 22 are still in place, along with dozens of flood alerts.
The number of flood warnings in place is expected to fall further, but the public should "remain alert" to the risk of flooding.
Gale and severe gale force westerly winds which will hit parts of the UK as Storm Barney comes in are expected to generate large waves around exposed coasts in south-west England and the English Channel tomorrow
But while some localised spray and waves coming over sea defences is possible, the overall coastal flood risk is very low, the Environment Agency said.
More than 20,000 homes were protected by Environment Agency flood schemes this weekend, according to the organisation which deployed more than 600 metres (2,000ft) of temporary defences with the help of 20 military personnel, to protect homes at Braystones, Whalley, Warwick Bridge and Ribchester.
Craig Woolhouse, director of incident management at the Environment Agency, said: "The flood risk will recede across northern England over the coming days, although river levels will remain high.
"The public should remain alert to the risk of flooding and stay away from raging rivers. With so much standing water around, we ask people to stay out of flood water and not attempt to walk or drive through it."