Amid sub-zero temperatures, the Met Office issued severe weather warnings, flagging up icy roads and drifting snow for the eastern side of the England as well as parts of Wales and Northern Ireland.
Forecasters warned the cold snap was expected to tighten its grip as the week continued, with temperatures dropping to minus 5C in some regions over the next few days.
It is expected to be the earliest major snowfall since 1993.
The Met Office said: "Snow showers have been falling all night across north-east Scotland, and down the east of England. There have also been some snow showers affecting Northern Ireland and parts of north Wales."
Worst-hit is forecast to be the Scottish Highlands - with up to 8ins (20cm) eventually settling in Grampian - and in Yorkshire, north-east England and East Anglia.
By the end of the week a moderate dusting of snow is expected across the rest of the country, though it will remain heaviest in Scotland, Orkney and the Shetland Isles.
Temperatures were not expected to rise much above 2-5C by day, remaining lower in the more exposed, rural areas.
Billy Payne, a forecaster with MeteoGroup, the weather division of the Press Association, said: "It's going to be a very cold day. There will be sleet and snow showers around, with the worst affected areas in northern and eastern Scotland and north-east England.
"There will be a covering of snow, especially over the higher ground, with wintry showers across London."
He added: "The cold spell looks set to stay at least into the beginning of December. There will be low temperatures into next week, with the risk of sleet and snow showers."
Motorists were urged to exercise caution on the roads as temperatures plunged and to check weather conditions before setting off.
The AA yesterday said it rescued a "handful" of cars stuck in snow in the Aberdeenshire and Moray areas, while call-outs were up significantly in North Yorkshire and Newcastle.
The organisation said it had attended around 7,500 breakdowns nationwide, with calls coming in at about 1,000 every hour by yesterday afternoon.
It predicted call outs could increase by half in worst-hit areas.
The impending snow sparked a surge in rock salt sales of 1,600%, DIY chain B&Q reported.
Wellington boots were also flying off the shelves, with sales up by 388% on last year's figure, and bosses said the store had stocked up on grit.
Tonight: Very cold with clear spells and wintry showers, these especially for northern and eastern Scotland, the east coast of England, Northern Ireland, Wales and south-west England, with just the odd wintry shower elsewhere. Further accumulations of snow are likely across northern and eastern Scotland and north-east England. A widespread, fairly sharp frost, with icy patches forming where the snow showers have fallen.
Tomorrow: Sunny spells with sleet or snow showers for some. These are most likely to affect Scotland and eastern England, more especially the coast, along with Northern Ireland, Wales, south-west England and perhaps the Midlands by evening. Slight accumulations of snow are likely, particularly over the high ground. Very cold with early frost and ice lingering in places.
UK Outlook (Saturday and Sunday): Bitterly cold over the weekend with sunny spells and a continued threat of sleet or snow showers. These are most likely to affect eastern areas, particularly eastern Scotland. However a few will spread to affect more western parts of the country, especially during Saturday. Accumulations of snow in places. Overnight frost and ice persisting all day in some areas.
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