Gusts of about 80mph hit some parts of the country, while gusts of up to 50mph were recorded in Glasgow at about 3pm, hitting shoppers out for the sales.
Thousands of homes in Dumfries and Galloway and the north lost electricity as trees and debris brought down power lines in the regions.
Thirteen flood warnings were in place, mainly in Tayside, with as much as 40mm of rain expected in some places.
And weather forecasters are predicting more rain in the run-up to the Bells.
Ben Windsor, forecaster at the MeteoGroup, said: "People can expect sunshine and showers in the afternoon.
"By midnight there will still be showers around and some of these might be heavy. But there will also be clear spells.
"Showers and clear spells will continue throughout the night and into Ne'erday."
Strong winds can be expected further north on the West Coast and Western Isles, but most of the country should not see gusts of more than 50mph over the celebrations.
This weekend, Glasgow residents can expect sunshine and showers, with heavy rain due to return on Sunday night.
Yesterday's severe weather led to trains being disrupted between Ardrossan South Beach and Kilwinning and services were affected in the Highlands and between Dundee and Aberdeen.
The strongest gusts of wind were in Inverbervie, Aberdeenshire (81mph) and in Dundrennan, Dumfries and Galloway (70mph). On the mountain tops the wind reached 93mph in the Cairngorms and 75mph in Glen Ogle, Perthshire.
In Stranraer the fire service had to weigh down a shed with paving stones that was being blown across gardens.
Many roads were blocked by fallen trees and others were flooded.
But the worst affected areas yesterday were Northern Ireland and south of the border.
Around 13,000 homes were still without power across south England and Wales, with thousands more affected in North Wales, Kent, Surrey and Sussex.
About 5000 customers in Northern Ireland were without electricity after severe gales with gusts of up to 75mph hit the country.
In south east England, Prime Minister David Cameron was confronted by an angry flood victim as he visited a village seriously affected by the storms.
Erica Olivares said her local council had done nothing to help villagers in Yalding, Kent, where homes had been severely damaged.
During the heated exchange Mr Cameron appeared rattled as he tried to defuse the confrontation by promising to contact the council himself.
In an angry confrontation with Mr Cameron in front of the television cameras, Ms Olivares said: "We still have no electric. We need electric. As I say, the council, from Monday, we have been trying to contact them, but they have all decided to go on their holidays. Nothing."
Geraldine Brown, chairwoman of Yalding Parish Council, said "We have an emergency plan that went into action and worked brilliantly.
"We went knocking on people's doors on Christmas Eve, warning people that this was going to happen, but some people are so pig-headed they stayed where they were."