A man has been killed by a falling tree in Kent as vicious gusts topping 100mph brought major disruption to Scotland, Northern Ireland, Wales and much of the western half of England from the Lake District to Cornwall.

Bridges have been closed, power lines cut and flights delayed or abandoned by the sudden but brief onslaught, which is expected to peter out by Tuesday afternoon, although with sporadic turbulence continuing on Wednesday and early Thursday.

The man in his 50s was crushed by an oak tree as he sat in the driver's seat of a parked van in Tunbridge Wells. Kent police said the man, from Tonbridge, was pronounced dead at the scene just after midday.

A spokesman said: "His van is believed to have been stationary at the time of the impact. A male passenger in the vehicle is not believed to have been injured."

Paul Harragan, who lives yards from the scene of the accident, said three branches had "completely crushed" the vehicle. "The van is completely crushed and there's a man with a chainsaw cutting the branches," he said.

Also in Kent, the Port of Dover was forced to close between 10.30am and 1.20pm because of high seas.

Heavy rain accompanied the gales in many areas in the first abrupt break from the exceptionally mild spell over the holiday, which saw the warmest and calmest Christmas for 14 years.

The worst effects have been felt on the British Isles' Atlantic coastline, with 105mph gusts recorded at Malin Head in Donegal and some 15,000 homes left without power in the area and neighbouring Sligo.

The Foyle bridge linking the two halves of Derry has closed along with exposed roads in the city and in Belfast, Omagh, Coleraine, Larne, Lurgan and Downpatrick.

Winds increased in strength as they tore across Scotland, uprooting trees, injuring four people at a caravan park where trailers overturned and closing the main bridges over the Forth, Clyde and Tay.

Gusts of 97mph recorded at Islay rose to 102mph at Blackford Hill in Edinburgh. Glasgow's civic Christmas tree was topped, and the Edinburgh-based crime writer Ian Rankin tweeted that his chimney pot was now in his garden.

Police in Strathclyde and Lothian and Borders advised people to travel only if their journeys are essential. The Met Office warned that mainland Scotland would have the worst of the storm, but added that Wales was also in the firing line with 93mph winds at Aberaeron in west Wales and the possibility of flooding from short but torrential falls of rain.

In Cumbria lorries were blown over on the M6 at Tebay and the trans-Pennine A66 and a gust of 106mph – Tuesday's highest so far – was recorded on the 848m (2782ft) summit of Great Dun Fell.

A bus driver with serious injuries had to be freed from his cab after a 6ft diameter tree fell on his single-decker Stagecoach service in Witley, Surrey, and the driver of a Ford Fiesta blown into a ditch at Tetbury in Gloucestershire is also being treated for serious injuries.

Disruption has been caused by tree falls in Camborne and Redruth in Cornwall and to rush-hour traffic in Greater Manchester, where a large tree blocked the main road through Marple and several others are in danger of collapsing nearby.

Rail links between Truro and Penzance have been halted by debris on the line and high-sided vehicles have been barred from the Tamar Bridge at Plymouth. Like Wales, Cornwall is vulnerable to flash-flooding after sudden, heavy rain and the Environment Agency has issued "yellow" flood alerts on 21 rivers.

The port of Dover in Kent announced that it had closed due to strong winds of force 11 in the Channel. A spokesman said ferry passengers should contact their operator before setting out to the port.

Dover and Dungeness lifeboats have been helping seven people on a yacht in distress in heavy seas off Kent, where Channel ferries are continuing to operate but with delays of an hour or more.

Temperatures in much of the country will remain at a relatively temperate 10C, but are expected to fall significantly in the north of Scotland, where snow is likely to fall on higher ground. There are severe weather warnings in place for most of southern and western England, west Wales, Northern Ireland and the bulk of Scotland, with the latter seeing more serious amber warnings.

A spokeswoman for Strathclyde police said they were called to Stratheck caravan park near Dunoon at 8.30am on Tuesday and four people were taken to hospital for treatment after their caravans were blown over. The Scottish transport minister, Keith Brown, denied that the storm had caught his staff on the hop.

He told BBC Radio Scotland that while amber alerts were issued on Monday evening, the red alert for the most damaging gusts in the central belt was issued by the Met Office at 8am on Tuesday. "By that time the winds had already got hold. The weather has not caught us out. We have to go on the advice we get from the Met."

A spokeswoman for the Met Office said that although the storm was seeing very high wind speeds, it was not unusual for the time of the year.

She said: "People are noticing it this more because they have had a really quiet winter. We have had a couple of snowy winters and when we get cold and snow you don't tend to get the big Atlantic storms. That's the difference between this year and last year."

East Coast Trains have stopped Edinburgh-bound services at Newcastle-upon-Tyne and replaced them with buses, which are also making the same journey south from the Scottish capital. A number of routes run by Caledonian ferries in the west of Scotland have been disrupted or cancelled.

Drivers planning to use the M25 Dartford crossing between Kent and Essex have been advised of possible delays. A Highways Agency spokesman said: "As a precaution, the east tunnel will be closed to northbound, anticlockwise traffic from 4am with the possibility of gales affecting the Queen Elizabeth II bridge which normally carries clockwise, southbound traffic from the M25 across the Thames."

While most of the rain will clear as the day goes on, the Met Office has renewed severe weather warnings for large parts of the west of Britain and Northern Ireland on Wednesday as another band of wet conditions passes through. Winds will remain strong into Thursday, though gradually easing.