On Sunday, a man in his 20s was pronounced dead in north London after the car he was driving was hit by a falling tree. It came hours after a 60-year-old man died in Dumfries and Galloway, in western Scotland.
Disruption to travel continued on Monday, and some schools in Scotland have been shut either due to lack of power, heating, water or damage.
Another weather warning has been issued by the Met Office for later this week. The yellow warning of wind, external, covers much of Scotland, as well as parts of northern England and Northern Ireland from 03:00 to 23:59 on Tuesday.
In Scotland, Network Rail said the Crianlarich to Oban and Inverness to Wick and Thurso lines remained closed, but work to restore them was ongoing.
ScotRail said the “vast majority” of its services were running as normal.
West coast ferry operator CalMac said some of its services could be cancelled at short notice, while passengers on NorthLink Ferries are advised that there is the “possibility of disruption” to services until Thursday.
Monday morning will bring rain to many parts of south-west England, Wales and Northern Ireland.
This will move quickly north-eastwards reaching central, eastern and northern England, as well as most of Scotland, by around lunchtime.
Winds will also strengthen throughout Monday, and it will turn even windier overnight as the area of low pressure passes close to Northern Ireland and north-west Scotland with gusts peaking on Tuesday.
While showers are forecast for Wednesday, conditions are expected to calm down midweek and most places will be dry by the end of the day.
Additional reporting by Ben Rich, lead weather presenter.