In both countries, the authorities have warned drivers to take extra care on the roads and motorists have been advised to check ahead before travelling.
The freezing weather has created dangerous conditions on the roads and may disrupt health and delivery services. Many motorists have been forced to abandon their cars after being snowed in.
The lowest recorded temperature was almost -5C in Perthshire overnight with widespread frost hitting large areas of the UK. The lowest recorded temperatures overnight were in areas where snow had already fallen, according to the BBC Weather Center.
Report informs referring to BBC, the UK's Met Office said there was a 90 percent chance of severe cold until New Year's Eve in parts of England, northern Scotland, Wales and Northern Ireland. The heaviest snow was in Leek, western central England.
French authorities said over 15,000 cars driving to and from the French Alps resorts were stuck due to heavy snow and the authorities were forced to open emergency shelters.
The harsh weather caused the death of a 27-year-old man whose car slid into a ravine in the Belledonne mountain range, French authorities said.
Meteo France, the French national meteorological service, declared an “orange weather” alert in 19 regional departments, especially in the French Alps.
They also said the bad weather will continue until Sunday night.
In a statement, France's Interior Minister Bernard Cazeneuve urged drivers "to exercise the utmost caution." He asked motorists not to take to the roads if possible.
The authorities warned of a high risk of avalanche in Haute-Savoie, a department in the Rhone-Alpes region of eastern France, bordering both Switzerland and Italy.