The Met Office has issued a number of weather warnings over the coming days, including a yellow warning for parts of the West Midlands, Shropshire and Mid Wales.
The forecaster extended the warning into today and tomorrow. Elsewhere, it warns of ice in coastal and northern England, and both snow and ice expected in northern Scotland.
Some roads and railways are likely to be affected with longer journey times expected, it said.
Icy conditions may result in some slips and falls and there may be icy patches on untreated roads, pavements and cycle paths, it added.
The UK Health Security Agency (UKHSA) has issued a Level 3 cold weather alert covering England from Wednesday evening through to Monday.
The RAC motor services company also urged people to keep blankets in their vehicles in case they break down in icy conditions.
Met Office chief meteorologist Steve Willington said: “As an Arctic maritime airmass settles across the UK, temperatures will fall with widespread overnight frosts, severe in places, and daytime temperatures only a few degrees above freezing.
“However, the cold air from the Arctic will also bring brighter conditions, with some dry, sunny spells, particularly away from the coast and where winds are light it could feel pleasant in the sunshine. Some patchy freezing fog is also likely. Showers will turn more wintry with an increasing risk of snow as the week progresses, particularly in coastal areas or over higher ground.”
MrWillington said temperatures in isolated parts of the UK will fall below -10C (14F) overnight over the next few days and areas such as the Shropshire Hills and Staffordshire Moors are expected to reach similar levels.
RAC spokesman Rod Dennis said caution and preparation were the key for drivers in the West Midlands. He said: “With temperatures plummeting this week, many drivers might be taken aback by the cold after an exceptionally mild autumn.
“Our advice is to be winter ready – check tyres are properly inflated and with good tread, while topping up oil, coolant and screen wash levels if needed. Drivers with older batteries in their cars might also wish to give their vehicle a 20-minute drive before colder conditions arrive to ensure the battery can cope with sub-zero temperatures.
“It’s also worth having a fully charged mobile phone and carrying a blanket in case of a breakdown to keep warm.”
The West Midlands branch of the charity Age UK advised people to maintain a supply of food and medicine to reduce the number of outdoor trips and have torches with spare batteries in case of a power cut.
Homeless people in London will be sheltered after the severe weather emergency protocol was activated for the first time this winter to provide emergency accommodation for rough sleepers.