Eurostar is running a restricted service and has said that any passengers turning up at St Pancras station, in London, would not be able to travel on Wednesday because all available seats had been allocated.
The company said that on Thursday it will be able to take everyone with tickets for either Thursday or from the past few days, on a first come first served basis.
Eurotunnel, meanwhile, said it was managing to clear the backlog of cars and lorries waiting to use its Channel Tunnel service.
Temperatures plummeted across the UK on Tuesday night and the early hours of Wednesday morning.
BBC weather forecaster Jay Wynne said the weather was getting worse on Wednesday evening.
He said: "I'm afraid we've got a spell of rain, sleet and snow moving north across the UK, and it's all going to freeze with another very cold night.
"North Wales, the north Midlands and northern England, that's all heavy snow and icy roads. It's going to get really quite treacherous out there."
But the forecaster predicted most people would have "a bit of a grey Christmas", with the chances of a white Christmas being "pretty slim", although there "might be a few flakes of snow in Lincolnshire and East Anglia".
About 5-10cms (2-4ins) of snow is forecast to fall in areas such as Lincolnshire, Nottinghamshire, Yorkshire, Humberside, Cumbria, Northumberland.
Predicted minimum temperatures for Wednesday night are:
• -2C (28F) in the Midlands
• -4C (25F) in northern England
• -10C (14F) in Glasgow
• -15C (5F) in rural Scotland
Scotland will have freezing fog as a result and Scottish Transport Minister Stewart Stevenson has said conditions on Scotland's roads are the worst for 20 years.
Dalwhinnie in the central Highlands looked to be one of the coldest spots this year at -16C (3F) - just short of the -18C (0F) recorded at Aviemore in February.
The Met Office has issued a number of warnings of "widespread icy roads" for most of England, Scotland and Northern Ireland.
Sections of the M27 have been closed following a number of accidents involving multiple vehicles, and some lorry drivers have reportedly pulled over to the hard shoulder of the motorway due to the icy conditions.
Police are currently trying to deal with numerous accidents across Lincolnshire, and North and North-east Lincolnshire. Two lorries are reported as having jack knifed, with some cars overturned because of the driving conditions.
Hampshire Police said there had been at least six accidents on the motorway in the Southampton area and warned motorists to take extreme care.
Buckinghamshire County Council has urged motorists who had previously abandoned their vehicles to collect them "as soon as possible". Thames Valley Police said abandoned cars were causing an obstruction in the High Wycombe area.
The AA said on Wednesday it was receiving 1,200 breakdown calls an hour and its president Edmund King accused some councils of not acting quickly enough to grit roads and claimed some "key roads" had "not been gritted at all".
Passengers queue to get limited places on Eurostar trains
The Local Government Association (LGA) said the claims were "unverified, unsubstantiated and unjustified".
But Cornwall County Council has confirmed that the road on which the fatal coach crash occurred in Townshend, near Hayle, had not been gritted because it was classed as a minor one.
Royal Mail said it was doing "everything possible" to ensure post arrives on time as it emerged thousands of online shoppers may not receive their goods by Christmas after snow crippled some deliveries.
Meanwhile, people have been urged not to travel to the Port of Dover unless they have a ticket, and ticketholders should check availability with their operator.
Problems persist on public transport in many parts of the UK. Major problems include:
• Queues of up to 30 miles on the M25 around London
• Heavy traffic in East Anglia, Cheltenham and Gloucester, Manchester, and Scotland
• Cancellations to Southern and Southeastern train services
• Some 200 out of 400 train services on the line between Hastings and London have been cancelled
• Delays and cancellations in Kent from Tonbridge to Strood and Ashford International
• Buses replaced trains in parts of south-east England
• Rush-hour delays from Glasgow Central to Edinburgh and Lockerbie after signalling problems in the Carstairs area
• All passengers are advised to contact their airline
• Fog meant British Airways had to cancel some short-haul flights from Heathrow, but its Gatwick flights were unaffected
• Easyjet cancelled more than 30 flights from the UK
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