Met Office forecasters said temperatures could plummet to -10C in Scotland on Saturday night with a low of -2 forecast for Sheffield.
Widespread frost could form on roads, causing travel headaches for thousands of motorists.
Dr Thomas Waite from Public Health England said heating homes to at least 18C, wearing several thin layers instead of fewer thicker ones and checking up on older people, young children and those with heart and lung conditions, would help to keep people well in the next few days.
The forecast comes as some UK communities were hoping for some much-needed respite after a second day of high winds in the wake of Storm Eleanor.
In Sheffield one couple had a lucky escape tonight after a tree was blown down and struck their car on Gresley Road, Lowedges.
Three people were injured by falling trees at the height of the storm on Wednesday and a body was found in the sea in East Sussex, although it was not initially clear whether they had been swept into the water by the storm.
The storm caused further chaos as it travelled across continental Europe yesterday, sparking rare forest fires in Corsica and closing ski resorts in the French Alps.
Public Health England has issued a warning ahead of the cold snap, which comes as the NHS is already struggling to cope with winter pressures.
Dr Thomas Waite, from the extreme events team, said: “When temperatures fall, the number of people having illnesses such as chest infections, heart attacks and strokes goes up – as their bodies struggle to work harder in colder conditions."
The Met Office issued a yellow severe warning yesterday across much of England and Wales as gusts reached up to 75mph.
The Environment Agency has also warned that parts of the country could be at risk of flooding following the persistent rain.