Temperatures were predicted to fall as low as minus 2C (25F) parts of Scotland and northern England on Monday morning as the autumn's first widespread grass frost spreads across the country.
Met Office forecaster Matthew Box said: "What we have is high pressure centred over parts of the UK, and that's bringing a northerly flow across, in particular, eastern parts of the UK, and it's brought northerly winds and polar maritime air mass across the UK throughout the course of Sunday as well.
"With that cooler air coming down and the high pressure moving slowly but surely eastwards into Sunday night, the combination of that cold air and the clear skies associated with that high pressure are going to allow temperatures to drop off.
As the day progresses, the coldest temperatures will be felt in Scotland at 9C (48.2F) to 10C (50F), while the south it will be a milder 12C (53.6F) to 13C (55.4F)
By Tuesday, the cold snap will thaw slightly, with maximum temperatures likely to rise one or two degrees.
The news came as forecasters claimed that this winter could be the coldest since 2012/13, when temperatures dropped to -14C.
Todd Crawford, of the Weather Company, said: “We expect the coldest winter in the UK since 2012-13.
“We expect extended spells with a ridge of pressure in the North Atlantic, especially in early winter. “This forces the jet stream up to the Arctic and back down into Europe, releasing Arctic high pressure from near the Pole directly into northern Europe, with colder-than-normal temperatures.”