The UK Health Security Agency (UKHSA) is continuing the warning until 9am on Thursday in the North East of England, North West of England, and Yorkshire and the Humber.
This morning, northern areas saw the mercury dip to 3C which may gradually go down to 0C.
The elderly and people with health conditions are being encouraged to keep their homes heated to counter the blistering conditions.
Dr Agostinho Sousa, of the UKHSA, said: “As cold weather persists throughout the rest of the week, it is important to check in on the wellbeing of those most vulnerable to the cold.
“Cold weather can have a serious impact on health, particularly older people and those with pre-existing health conditions, as it increases the risks of heart attacks, strokes and chest infections.
“If you have a pre-existing medical condition or are over the age of 65, it is important to try and heat your home to at least 18°C if you can.”
The three areas of the north are under a Level 3 weather alert, while the West Midlands, East Midlands and East of England have a Level 2 alert in place.
Earlier snowfall in the North is expected to drift south to cover the Midlands on Tuesday and Wednesday.
At the same time southern England will shiver in strong winds and freezing rain, with highs of just 4C to 7C expected.
The Met Office added: “A band of rain will gradually turn to snow from the north during Monday morning, initially above 200m, but later, to low-levels. 2-4 cm are possible above 200m and 5-10 cm above 300m.
“A few cms may develop locally at lower levels into the evening. Rain and snow should clear to the south of the area Monday evening, and with skies clearing, icy stretches will be possible on untreated surfaces.
“Occasional snow showers will follow into the north and west of Scotland during Monday evening and night giving a few cm of snow in places.”