The hospice ambulance driver died and his passenger was badly injured on the A688 in County Durham. Nearby, a collapsed roof crushed a dozen cars.
Further north, in Ayrshire and Dumfries and Galloway, several hundred homes are without power, says Scottish Power.
Worst-hit are southern and central parts of Scotland, Northern Ireland, and northern England and Wales.
The Met Office has issued severe weather warnings for many areas and flood alerts have been issued, with road, rail and ferry travel disrupted.
The death of the driver happened at about 15:00 BST near Dunhouse Quarry, between Staindrop and Barnard Castle.
He has not been named, but was a volunteer with Butterwick Hospice in Bishop Auckland.
Graham Leggatt-Chidgey, chief executive of the hospice, said: "We can confirm that one of our long-term volunteers has been killed.
"We and the police are liaising with the man's family at the moment."
The passenger's injuries are not thought to be life threatening.
Also in the North East, cars were crushed when the roof of a building on Littleburn Industrial Estate at Langley Moor collapsed in strong winds.
In Scotland, a lorry hit a tree on the A811 near Arnprior, Stirlingshire, causing the telegraph pole to collapse. Power has been restored.
No-one was hurt in either incident.
A catering marquee being used on the set of the TV series Game of Thrones was ripped into the air near the Carrick-a-rede Rope Bridge on the north coast of Northern Ireland.
The weather caused the cancellation of stage two of cycling's Tour of Britain, through Lancashire and Cumbria.
"We've had to take the decision based on the advice we've had from the police and highways [officials] that it is unsafe," a tour spokesman said.
In Cornwall, the RNLI was warning surfers of the dangerous conditions caused by strong winds as a body boarder was rescued after being swept onto rocks.
The Met Office issued an amber warning covering several areas, meaning the public should be prepared for the risk of transport disruption and the possibility of damage to trees and structures.
It said an 82mph (132km/h) gust had been recorded at Capel Curig in north Wales, with strong winds expected to continue into Monday evening.
BBC weather forecaster Laura Tobin said: "We have some very stormy weather outside... courtesy of a deep area of low pressure. It is the remnants of Hurricane Katia.
"We could have gusts of wind up to 70mph (113km/h), maybe even 80mph around exposed headlands, coasts and hills."
She said the strong winds would decrease a little overnight and throughout Tuesday, and ease off completely by the end of the week.
Heavy rain in western Scotland is expected to continue for several days, giving a risk of localised flooding, with the Scottish Environment Protection Agency issuing several alerts.
The Environment Agency has alerts in place near Bridlington in East Yorkshire, Derwentwater in Cumbria and the western coast of Anglesey.
Some rail services in Scotland and northern England have been hit by delays and cancellations, National Rail Enquiries warns.
East Coast train services between London King's Cross and Newcastle have been seriously affected with some services cancelled after a tree fell on to the track between Durham and Darlington. Delays are expected until at least 23:00 BST.
Replacement coach services are operating between Darlington, Durham and Newcastle until the line reopens.
National Rail is updating its Twitter feed with the latest train disruptions.
ScotRail said there was some disruption to trains services between Glasgow Central and Largs/Ardrossan. Replacement buses were being provided from Kilwinning.
Other reported travel disruption included the cancellation of some Irish Sea ferry crossings, while in Scotland Caledonian MacBrayne has cancelled some ferries including services to and from Oban, Arran, Islay and Cumbrae.
The Severn Bridge has been closed to high-sided vehicles, along with the A55 Britannia Bridge to Anglesey and the Foyle Bridge in Londonderry.
In Scotland, the Tay Bridge has a 30mph limit and the Forth Road Bridge has a 40mph limit and is only open to cars.
Power companies have extra call handlers and engineers on standby to deal with any problems caused to electricity lines by the severe gales and possible falling trees.
People have also been urged to secure items such as garden furniture, wheelie bins and trampolines or store them safely.
A motorist has been killed by a falling tree as fierce winds from the tail-end of Hurricane Katia batter the UK.