BBC forecasters say freezing temperatures will last until at least Wednesday and probably longer.
Roads remain treacherous and the government has begun prioritising areas for new salt supplies.
The Highways Agency has already stopped treating motorway hard shoulders in England and the government has ordered salt from abroad but this is not due to arrive until 21 January.
The agency's David Grunwell said the motorway and trunk road network was "running remarkably well" and that it had sufficient salt stocks for the conditions.
The Conservatives have said the move to ration salt is "an admission of utter failure" and plans should have been made earlier.
Edmund King, president of the AA, said he had raised concerns about salt supplies before Christmas.
"We were not assured that everyone was as prepared as they should have been that's why I wrote to the Local Government Association in November."
But David Sparks, of the LGA - which represents councils in England and Wales with responsibility for local roads, said people would still be able to travel.
"The major roads will be gritted, the major communications between the country, and within local authorities and regions. We have done everything we can do," he said.
York council has begun mixing sand into its road salt to make supplies go further, although the move renders the grit less effective.
In south Wales, Rhondda Cynon Taf council is treating 40% fewer roads and closing mountain routes. Caerphilly, Cardiff and the Vale of Glamorgan councils will run out of salt by Monday if weekend deliveries do not arrive.
WEATHER AND TRAVEL INFO
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Professor Stephen Glaister, director of the RAC Foundation, said the onus was not solely on the authorities, who had limited time and money.
"Drivers need to act responsibly too, lower their travel expectations and be ready for the worst - that might mean people routinely having to have things like snow chains."
Lane closures are in place on the Severn Bridge, the M58 near Wigan, the A1 (M) near Harrogate, North Yorks, and the M6 north of Warrington. The westbound A174 is closed near Redcar, Cleveland, after a lorry jack-knifed.
British Airways has cancelled 54 flights at Heathrow on Saturday. It is warning customers to check its website for delays and cancellations and not travel to the airport if flights are cancelled
Eurostar is running about two-thirds of its normal Saturday service from London and plans a restricted service on Sunday
The Association of Train Operating Companies says a full service is planned for Monday but disruptions are still affecting nine operators' services
First TransPennine Express has cancelled all trains between Manchester Airport, York and Newcastle. Buses replace East Coast trains between Edinburgh and Glasgow Central, Inverness and Perth, and Dundee and Aberdeen
The weather is also causing major disruption to sporting fixtures, with all but two of the weekend's Premier League games called off, a number of race meetings cancelled, and several rugby union matches postponed.
Around 400 houses are without gas around Mortehoe, North Devon, after water got into the main supply pipe, Wales and West Utilties has said.
Energy supplier EDF has said about 200 homes near Luton, Beds, are still without electricity after power cuts affected 500 customers overnight.
Retail research group Synovate said the weather was having an impact on shopping, with 28% fewer people entering non-food stores between 6 January and 8 January compared with the same period last year.
The worst affected regions were south-east and southern England, where numbers were down by 35% year-on-year.
BBC weather forecaster Alex Deakin said eastern England would see 2cm-5cm (0.8in-2in) of snow on Saturday, with up to 10cm (4in) in the South East on Saturday night, in particular south and east of London.
Snow showers will move across England and Wales on Sunday, with falls of 2cm-5cm or 10cm on high ground, he added. Temperatures on Sunday should be around freezing.
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