Scotland and northern England were the worst-affected areas with a top wind speed of 151mph recorded on the summit of the Cairngorms in Aberdeenshire, the Met Office said.
Thousands of schools across all but six of Scotland's 32 local authorities were shut by lunchtime to allow pupils to get home safely.
Glasgow was one of the worst-hit areas, with 71mph winds recorded at lunchtime.
The University of Glasgow and Caledonian University were closed, as were all public museums, galleries, sports centres and libraries.
Cumbria saw heavy rain, and police said they received several calls from motorists stuck in floodwater in Ambleside, Windermere, Troutbeck and Selside. The Environment Agency issued seven flood alerts at different locations on 12 rivers and lakes in the county.
Royal engagements in Scotland and the North East were cancelled because of dangerous winds.
The Countess of Wessex postponed two visits in County Durham - to Billinghamtown and a meeting in Durham relating to her role as patron of Sunderland Association Football Club Foundation.
A Buckingham Palace spokesman said the bad weather meant her flight was cancelled but she instead took a train and was able to take part in events later today.
The Duke of Gloucester postponed a day of engagements in Glasgow.
Strathclyde Police said more than 100 weather-related incidents had been reported to them during the day and Chief Inspector Stewart Campbell said people should only travel if their journey was essential, advising them to stay indoors.
The travel warning stretched across the central belt, from Strathclyde to Lothian and Borders, and also applied to pedestrians who may be at risk of being hit by objects blown by high winds.
Earlier a school bus overturned on the A737 in Dalry. Only the driver was on board and he escaped with minor injuries.
Wind also blew over an articulated lorry on the A87 in Glenshiel in the Highlands, but the driver was not hurt.
And a large tree fell on a vehicle in the car park at Queensferry Hotel in North Queensferry, Fife, this morning. The driver was unhurt but left shaken.
Strong winds forced the closure of every major bridge in Scotland: the Forth Road Bridge between Edinburgh and Fife; the Erskine Bridge, which connects Renfrewshire and Dunbartonshire; the Skye Bridge; and Tay Road Bridge.
Flights to and from Scotland were also disrupted. Glasgow and Edinburgh each had 17 flights cancelled and a further four planes had to be diverted from Edinburgh.
Passengers have been advised to check the status of their flight before going to the airport.
ScotRail put a speed restriction of 50mph in place on all trains in case of falling trees or other debris and due to the risk of damage to overhead power lines.
Trains between Aberdeen and Inverurie, Glasgow and Dunblane, and Edinburgh and Glenrothes were cancelled, while other services ran less frequently.
Caledonian MacBrayne ferries to the western islands of North Uist, Harris, Mull, Islay, Gigha, Coll, Tiree and Arran were all cancelled, while other ferry timetables have been severely disrupted.
Strong winds gusting to force 10 were experienced in the English Channel, causing poor visibility and disruption to ferry travellers.
The Port of Dover said all services with P&O Ferries to Calais and DFDS Seaways to Dunkirk were subject to delays because of bad weather.
However, the high-speed winds are expected to ease by tomorrow morning throughout most of the UK.
Aisling Creevey, a forecaster at MeteoGroup, the weather division of the Press Association, said: "The storm system is moving away overnight and by tomorrow morning the worst of the winds will just be in the north-east of Scotland and Northern Isles.
"The winds will ease significantly tomorrow across much of England, Wales, Northern Ireland and the rest of Scotland."
Most of Scotland is unlikely to see temperatures rise much above freezing with snow expected on higher ground, and a cold and icy start to the day is expected in northern England and Northern Ireland.
There may be wintry showers in Scotland and in parts of western areas, north-east England and Yorkshire.
PA
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