Motorists have been warned of bridge and road closures during rush-hour and some ferry and rail services remain suspended.
Winds of 90mph were recorded in South Uist overnight, with gusts of 60mph in Glasgow and 63mph in Loftus, North Yorkshire.
Around 2,000 homes in the north of Scotland remain without power. Since the start of the storm on Monday afternoon Scottish Hydro said engineers have reconnected 9,000 properties which lost electricity.
The severe weather created difficulties for recovery teams attending to blown-over vehicles, routes blocked by trees and buildings made unsafe by the extreme winds.
Met Office amber “be prepared” warnings were still in place until 9am on Tuesday.
Henry is the eighth winter storm and comes days after the UK saw off Storm Gertrude, which brought gusts of more than 100mph in Shetland.
Gusts of 84mph forced the closure of the Forth Road Bridge on Monday, and travel on the A82 between Glencoe and Rannoch Moor was restricted after a van and a lorry were blown off the road.
The Tay Bridge was shut and roads operator Bear Scotland said motorists should be aware of likely closures on the Skye, Kessock, Dornoch and Cromarty bridges.
The Humber Bridge near Hull was also closed to high-sided vehicles and caravans and a speed limit was imposed after a lorry blew over in 49mph winds.
Warnings for wind at the lesser yellow “be aware” level remain in place for Northern Ireland, Wales, northern England and the West Midlands.
Storm Henry also risks further flooding in Scotland, where almost 30 flood warnings are in place across the regions.
Pascal Lardet from the Scottish Environment Protection Agency said: “There is a coastal flood risk for the Western Isles, due to storm force winds generating a large surge and waves.
“Flooding impacts could include disruption to travel, particularly causeways, from spray and wave overtopping. Elsewhere tides are currently low, however minimal impact from wave overtopping and spray is possible along exposed northern and western coastlines until Tuesday.”
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