Forecasters warned that temperatures will hover around 0C (32F) for most of the day, before plunging as low as -7C (19.4F) in some places tonight.
Aisling Creevey, a forecaster with MeteoGroup, the weather division of the Press Association, said: "Today is going to be very cold, with temperatures of between 0C (32F) and 3C (37.4F) in most of the UK.
"Tonight it will be bitterly cold, between -4C (24.8F) and -7C (19.4F).
"We'll see a maximum temperature of 2C (35.6F) tomorrow, with penetrating ground frost overnight."
However, Ms Creevey said there was little snow forecast today, apart from the chance of snow flurries on the North Sea coast and show showers in the same area tomorrow.
She added: "Friday is the day we are keeping an eye on. Eastern England could see snow showers, with a couple of centimetres of snow in Kent. But there is a lot of uncertainty at the moment."
An Atlantic front may also move into Scotland from the west on Saturday, which could result in 5-10cm of snow across higher ground.
The below average temperatures are likely to remain for the rest of the week, and milder weather is not expected until Monday.
A charity which cares for the elderly warned that winter brings risks for them.
Michelle Mitchell, charity director general at Age UK, said: "It may have been relatively mild so far this year but the winter can be a dangerous time for older people. Many people believe that the only risk of winter weather is getting a cold but the risk is much greater. Low temperatures raise blood pressure which puts people at a greater risk of heart attacks and strokes as well as increasing the likelihood and severity of flu and other respiratory problems.
"We want older people to be able to enjoy the winter and, most importantly of all, stay well. That is why we have linked up with the Met Office to get advance information to ensure that forewarned is forearmed when it comes to winter weather."
The Department of Health has advised people to check local weather forecasts for the latest information on weather conditions and staying safe when outdoors.
A spokesman has said: "We are working closely with the NHS and local authorities to ensure vulnerable people stay well during cold weather and get the help they need within their communities."