The snow is expected to head south later in the week Siberian winds are set to cause further disruption during the UK’s “big freeze” by blowing snow back into cleared areas, forecasters warn.
Parts of eastern England and Scotland already under thick snow could see up to 25cm (10in) more overnight.
BBC meteorologist Philip Avery said it was likely the strong winds would cause significant drifting.
Meanwhile, the Local Government Association said councils had increased stockpiles of salt and grit this year.
Mr Avery warned that plummeting temperatures overnight on Monday were likely to lead to icy roads in many places, while the strengthening winds will make it feel even colder.
The UK has been experiencing the earliest widespread snowfall since 1993.
Met Office severe weather warnings for heavy snow and icy roads are in place for central and eastern Scotland, including the Borders, and north east England down to the east Midlands.
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There are early warnings of more to come on Monday and Tuesday, with eastern counties again the most at risk.
Mr Avery said the worst weather would be in central and eastern Scotland and north eastern England but added: “There is a likelihood of wind in the northern half of the British Isles picking up in strength leading to more significant drifting.”
But for some regions, Monday’s forecast is for a nicer day, he said.
“For many areas, for example, the western end of Cornwall, west Devon and the western side of Wales, it will be dry, fine and sunny.”
But, he warned the biting winds would have an impact and make it feel colder than it was.
The Greater London area and Kent are at risk of snowfall from Tuesday, with the Met Office warning that drifting snow could cause disruption to road and rail networks towards the end of the week.
David Sparks from the Local Government Association said councils are prepared this year to cope with the winter weather.
Councils boost salt and grit stockpile in big freeze
He told the BBC: “Local authorities this year have made unprecedented preparations for the winter.
“We’ve got well over a third more salt and grit in our stocks than we had last year and over a half of local authorities have invested in new gritting lorries.”
He added that individuals also had to make their own preparations and added: “What everyone needs to realise is that you cannot control or battle with the weather if it is unprecedented. You need to try to mitigate the effects.”
But motoring organisations the AA and the RAC warned commuters to continue to take great care, even on major roads that have been gritted.
AA spokesman Gavin Hill-Smith said the organisation had experienced “virtually unheard of” numbers of call-outs on Sunday and patrols were expecting even more on Monday morning.
“A lot of cars haven’t been used over the weekend, but when people come to go to work or school on Monday they’ll find the battery is flat or they can’t get out of the drive,” he said.
He warned people to take extra care: “The main concern is always ice. People must not get complacent – even on major roads that have been treated patches of ice can still develop.
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“They also need to leave themselves extra time in the morning – for the drive itself and to make sure the car is completely clear of snow and ice before they set off.”
A number of airports, including Edinburgh, Glasgow, Derry, Newcastle and Durham-Tees Valley, were affected over the weekend and disruption is likely to continue on Monday.
Rail and bus services in parts of Scotland and north-east England are also likely to face further problems.
On Saturday night temperatures in Wales and Northern Ireland fell to the lowest on record for November, reaching -18C (0F) and -9.5C (15F) respectively.
The unusual weather is being caused by high pressure over Greenland and low pressure in the Baltic states, forcing cold winds from the north-east across Europe.
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