The cold spell, bringing below-zero temperatures and snowfalls of up between 10 and 40 cm, also affected the northern half of France and Belgium.
In Britain, London's main Heathrow airport was closed as British Airways (BA) and other airlines cancelled up to 800 flights.
A Cyprus Airways airliner slipped off the runway at Heathrow airport Monday, but all passengers escaped unharmed, the airport authorities said.
The plane was the last to land at Heathrow Monday before the airport was closed to traffic due to severe weather conditions.
London's City airport was closed, while Gatwick and Stansted operated at reduced capacity.
Forecasters have said there will be more snow over the next two days, affecting mainly southeast England, Wales and Scotland in what they said were the heaviest snowfalls since 1991.
Drivers and users of the rail network were warned to undertake only essential journeys as the ambulance service said it would only respond to "life-threatening" call-outs.
Authorities said an estimated six million people failed to make it to their place of work, as thousands of schools remained closed.
Trading at the London Stock Exchange (LSE) was at the third of its normal level.
Two climbers died on Mount Snowdon, in Wales, police said. The bodies of the two brothers were found after mountain rescue crews and the Royal Air Force were alerted late Sunday.
In London, all bus services were cancelled and only one out of 11 Underground (Tube) services were running. The buses carry six million passengers a day, and 3 million journeys are made daily on the Tube.
Schoolchildren, however, enjoyed snowball fights as some people took to skiing in London shopping streets. Most shops, however, remained closed.
"Such a widespread coverage of snow has not been seen in the UK since February 1991 when there was extensive and heavy snowfall between February 7 and 9," said Helen Chivers, a forecaster with the Meteorological Office.
Conditions would get worse over the next 24 hours as more wintry weather arrived from northern France, she said.
Heavy snowfalls were reported from eastern Britain as temperatures fell below zero, bringing the risk of icy roads. Scotland was also bracing itself for severe weather.
In France, the hazardous conditions caused traffic jams of more than 225 km on motorways into Paris and slowed traffic to a crawl in the city itself.
Bus traffic in some Paris suburbs was reported at a standstill because of the snowfall, which totalled up to 5 cm in some locations.
BFM television reported that 15 to 25 percent of scheduled short- and medium-haul flights were cancelled at the city's two main airports, which also reported average delays of about 30 minutes.
As temperatures rose above freezing, the snow turned into freezing rain, making driving conditions more hazardous.