The UK is braced for more storms overnight which will strike the country further north than on Monday.
Forecasters are predicting gales of up to 80mph affecting Northern Ireland and the north of England and Wales, and possibly snow in northern England.
They expect wind to disrupt rush-hour traffic on roads in the north of England such as the M6 and the A1.
The clear-up has started after Monday's winds which affected transport and left about 30,000 homes without power.
BBC weather forecaster Chris Fawkes said: "The wind will start to pick up about midnight in Northern Ireland and then strong winds will spread to the rest of northern England and Wales, and will pick up elsewhere too.
"There's also the potential for some snow in parts of northern England.
"In tomorrow's rush-hour we could have disruption to some of the northern roads like the M6 and the A1 with strong gusts of wind.
"These winds have the potential to disrupt transport quite easily. We almost quite expect it."
He said Monday's weather included a 95mph gust of wind at The Needles on the Isle of Wight.
The Environment Agency has three flood warnings and 39 flood watches in place.
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It was the most dreadful storm I have ever driven through with driving rain and gale force winds
The flood warnings are for the Broad and Earnley Rifes at Selsey in West Sussex, Chichester Harbour east of Emsworth Channel, and Lands End to Hartland Point in Devon.
The Met Office has severe weather warnings for Tuesday and Wednesday for most of the UK apart from southern England, south Wales, and northern Scotland.
The Energy Networks Association, which represents UK energy suppliers, said about 2,400 homes in south-east England, 1,900 in east England and 3,000 in south-west England were still without power.
The prestigious Cheltenham horse racing festival started on time at 1400 GMT after the course survived Monday's storms.
On Monday, a number of flights at Heathrow and Gatwick airports were cancelled, and speed restrictions were put in place on some rail lines.
The Port of Dover was closed, with P&O Ferries unable to operate any of its Dover-Calais sailings.
Flooding caused lane closures on the M25, and the RAC warned drivers to be prepared for hazardous driving conditions over the next few days.
The M48 Severn Bridge between England and Wales was closed both ways because of high winds.
Gusts also caused considerable damage and disruption, blowing off garage roofs in Devon and west Wales, uprooting trees and bringing down power lines.