Weather warnings are in place for most of the UK, as forecasters say another storm system could hit this week.
The Met Office issued yellow "be aware" warnings for wind and rain for all regions except Eastern England and Orkney and Shetland.
Severe weather warnings of snow were also issued for eight regions of Scotland for 24 hours from 03:00 GMT.
The Met Office said one of the stormiest periods the UK has seen for several years was set to continue.
Chief forecaster Tim Hewson said: "There is some uncertainty in the forecast for later in the week, but there is potential for a significant storm and we are keeping a close eye on the situation as it develops.
"We'll be regularly updating our forecasts and warnings, so we advise everyone to stay up to date with the latest situation."
Wednesday is predicted to be "bright and breezy" for most places, ahead of the potential arrival of another storm system on Thursday and into Friday.
Early on Tuesday, according to the Met Office, heavy showers could fall as snow on hills above 100m in Scotland, Northern Ireland and the East Midlands.
There could also be slushy snow at lower levels and some roads could become icy, it said.
Scotland's transport minister Keith Brown has warned that snow and high winds could lead to evening rush-hour disruption for drivers on Tuesday.
Environment Agency Wales (EAW) has advised people to remain alert for localised flooding, with heavy rain and strong winds forecast. EAW said parts of south Wales were expected to be worst affected.
BBC Wales weather presenter Behnaz Akhgar said gusts of up to 70mph (112km/h) were possible on exposed coastlines and high ground.
Winds were already gusting in excess of 60mph in south-west England and the south coast on Monday evening, forcing the closure of the Tamar Bridge between Devon and Cornwall on Monday before it was later reopened.
Hampshire Fire and Rescue Service was called to rescue a man after the collapse of a tree had trapped him in the bedroom of his Winchester home.
Tom Tobler, of Meteogroup, said Thursday going into Friday could see "the strongest winds of the week".
The Environment Agency has flood warnings in place - meaning that flooding is expected and immediate action required - mainly around rivers in south-west England.
In the South West warnings have been issued for the River Wriggle, the River Dart from Buckfastleigh to Totnes, the River Torridge from Dolton to Bideford and the River Axe from Winsham to Axminster.
Isolated minor flooding was reported in parts of the South West on Tuesday morning, and motorists have been warned to look out for excess water and fallen debris on the roads.
In the North East a flood warning was issued for the River Swale at the Brompton-on-Swale caravan park.
The Scottish Environment Protection Agency also issued flood warnings for areas in Argyll and Bute, Ayrshire and Arran and West Central Scotland.
The severe weather resulted in the cancellation of Brittany Ferries services to and from France, but the company says these have now been restored and are running normally.
Go to the BBC weather page for more detailed information on your area, or click on the cities on the map below.