The AA dealt with double the normal number of breakdowns between midnight and 9am, and said that roads could be "very busy and dangerous" due to the weather.
President Edmund King said: "Extremely difficult travel conditions persist across many parts of the UK as millions of drivers, who have not yet done so, travel to family and friends for Christmas.
"Many roads today are expected to be very busy and dangerous due to snow and black ice. If drivers can reasonably delay any non-essential trips until Christmas Day or Boxing Day the weather and traffic should be better."
A rise in temperatures meant conditions eased in some areas, but a number of accidents led to delays on main routes.
Part of the A180 in Lincolnshire was closed after an accident and there was also a part-closure of the A66 in County Durham.
A broken-down vehicle caused delays on the M40 in Warwickshire, and there were also delays on the M25.
The Highways Agency, which is responsible for England's motorways and major A roads, lifted roadworks at 44 sites from 6am today until midnight on 3 January.
David Grunwell from the agency said: "Conditions are very challenging. Many people are travelling long distances, longer than they would normally. The key is very much to be prepared for the journey."
There were delays and cancellations at most of the major UK airports and budget airline easyJet had to cancel 16 Christmas Eve flights.
British Airways said its services were running normally at Heathrow, with the west London airport expected to handle around 144,000 passengers today.
But passengers on a London to Belfast Aer Lingus flight that should have left Heathrow at 3pm yesterday were still waiting to get away at noon today.
Police were called to calm angry passengers berating check-in staff at Manchester Airport after their flight was cancelled today.
An airport spokesman said the cancellation of the easyJet flight to Alicante, Spain, sparked anger among some passengers when they learned the news. He said: "Police were in attendance when check-in staff were sorting out the implications for travellers. It's something that happens frequently, police are often in attendance when flights are offloaded."
The spokesman said he believed around 100 passengers were affected.
He said KLM and Air France flights were cancelled earlier today but passengers had been rerouted on to other flights.
The spokesman said the airport was operating normally and has accepted a diverted aircraft travelling from Exeter to Leeds Bradford Airport.
Liverpool John Lennon Airport was operating normally, with flights "more or less on schedule" according to a spokeswoman, who said they were accepting diverted flights from Leeds Bradford Airport. She said: "We've had no significant problems, we're just hoping the fog doesn't come down later."
Eurostar was running around two-thirds of its normal high-speed Channel Tunnel trains between London and Paris and Brussels.
The company, which had to suspend services for three days following tunnel breakdowns last weekend, urged passengers with tickets for travel today to turn up at St Pancras station an hour before departure.
Eurostar also said that anyone with tickets for December 19-23 would be able to travel today.
"We're hoping to get everyone away for Christmas today," said a Eurostar spokeswoman.
The company added that it was planning to run a "near normal" service on December 26 and 27, including ski services.
On domestic railways, the bad weather led to the axing of a number of services from Glasgow Central station.
A broken-down train at Guiseley resulted in delays in West Yorkshire between Ilkley and Leeds/Bradford Forster Square.
Signalling problems in the Slade Green area of Kent meant services run by the Southeastern train company were delayed, and a broken-down engine in the Stratford area of east London resulted in delays to National Express East Anglia services.
Those who have bet on a white Christmas are likely to miss out, with most areas expected to be warmer and brighter on Christmas Day.
Rob Hutchinson, of the Press Association's weather division MeteoGroup, said: "December 25 is likely to be a dry day in most areas. There could be some snow in north-east Scotland and sleet or snow might edge into Wales and north-west England later in the day."
He said that Christmas Day temperatures would range from around 8C (46F) in southern areas to around 0C (32F) in parts of Scotland.
It will struggle to get above freezing in parts of Scotland and northern England on Boxing Day, but it could reach 10C (50F) in southern England.
Mr Hutchinson added: "After that, it looks as if it will turn cold again, with northerly winds."
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