A major crash involving a double-decker bus and a motorcyclist on the A39 in Somerset caused a road closure just a few hours after the police force dealt with 53 crashes on Monday evening.
Avon and Somerset police warned drivers to stay at home and avoid all but essential travel after ice hit on Monday evening.
Further south, snow and ice warnings were in place for usually mild Devon and Cornwall.
Between 6pm and 11pm on Monday, Avon and Somerset police also dealt 67 other road-related incidents, most of them the result of the freezing weather.
“We are advising the public to only travel where absolutely essential due to the treacherous driving conditions. If travel is necessary, we ask the public to take extreme caution and allow additional time to trave,” Superintendent Mark Runacres said.
“We have seen a significantly higher number of road-related collisions and incidents in the past 12 hours, which has increased the demand on police resources. We are working with local authorities and National Highways to ensure roads are gritted ahead of the rush hour traffic.”
“A significant number of police, fire and ambulance units are on the scene and a major incident has been declared,” police said after the crash involving a double-decker bus.
The force said: “Please only travel if it is absolutely essential. The conditions are extremely icy and dangerous due to the freezing conditions overnight and residual water on the road from the past week's wet weather.”
All of England will continue to experience cold weather until 9am on Friday, the Met Office has warned.
At just after 3am, Devon and Cornwall Police tweeted: “Police are urging drivers to travel with caution as heavy snow showers sweep across the region.”
By 4.30am there were reports of vehicles stuck in snow.
Mayor of London Sadiq Khan activated the capital's Severe Weather Emergency Protocol to provide emergency accommodation to people on Monday, as temperatures in the city were expected to fall below 0°C overnight.
The Met Office said "snow showers and icy stretches may bring some disruption" and could lead to longer journeys for drivers and train passengers.
It said treacherous weather conditions could also lead to slips and falls on icy surfaces, and urged drivers and cyclists to beware of icy patches on untreated roads.
The Met Office has also issued a yellow warning for snow and ice across parts of Northern Ireland, north-west England and Wales from 12pm on Monday until 12pm on Tuesday. Separate yellow warnings for snow and ice are in place in Scotland until 9am on Tuesday.