"It is nowhere near the UK's record low of minus 27.2C (minus 17F) but it will still be very chilly."
The Grampians, eastern parts of the Southern Uplands, the Lake District and the Pennines are expected to be hit hardest. Wales, the Midlands, East Anglia and parts of the South East may also wake to a covering of up to one inch of snow on Wednesday morning and overnight frost is expected throughout the country.
Issuing a yellow warning for ice on Monday and Tuesday, the Met Office said slippery stretches are "likely on untreated roads and pavements".
Mr Conlan said the cold snap should let up after Wednesday, with indications that temperatures may warm up as milder winds come in from the South West on Friday.
Police closed the A66 across the Pennines between Bowes, County Durham, and Stainmore, Cumbria, because of heavy snow. A Durham Police spokeswoman said: "There are currently tailbacks of traffic while this process is under way."