Half of the UK's local authorities only have enough road salt for six days of continuous freezing, the AA has said.
The motoring organisation said it understood councils had 250,000 tonnes less road salt in stock than they would have had a decade ago.
But the Local Government Association said the suggestion councils were not ready was "ridiculous scaremongering".
Forecasters are warning of very cold weather this week, with ice and snow likely in east and central England.
BBC weather presenter Sarah Keith-Lucas said temperatures could fall as low as minus two overnight on Monday, with ice likely on roads in parts of south east England and East Anglia on Tuesday morning.
Sleet and snow is possible from Monday on higher ground, particularly over the Pennines, with a larger area of eastern and central England at risk on Tuesday.
More freezing conditions are forecast later in the week with a further influx of sleet and snow due to spread towards the west of the UK.
'Just in time'
The AA said it had been informed of the salt shortage by industry sources.
It said last winter's heavy snow meant stocks had dwindled and some councils had to "borrow" from others.
The organisation added local authorities' reliance on "just in time" deliveries left too many of them vulnerable to a lengthy big freeze or major snowfall.
AA president Edmund King said: "Around 1,000 people are killed or seriously injured on snowy and icy roads each winter and hospital casualty departments are often inundated with people who have slipped and fallen.
"We accept that not every road can be treated, but we must do a lot more to keep the wheels of the economy turning in winter emergencies and 'routine' winter weather. That means getting enough salt stocks in place now."
Mr King told BBC Radio 4's Today programme it was "pretty chaotic" in February when councils were unable to cope with a deep freeze on the roads.
"There was a 25% increase in hospital admissions, the economy lost £1.2bn because of the chaos. Hospitals, schools and refuse collections were all affected," he said.
But Councillor David Sparks of the Local Government Association - which represents councils in England and Wales - rejected the AA's claims.
He told the Today programme it was "ridiculous" for the AA to focus solely on the amount of salt, which could be increased within 48 hours and moved around the country.
"It is ridiculous scaremongering for the AA to suggest that councils are not prepared for prolonged winter weather," he said.
"If the AA thinks the only way councils can ensure they have enough salt is by stockpiling it, it is showing startling ignorance.
"Councils realise how important it is to keep roads clear. It's up to councils, not the AA, to decide whether it is a good use of their council taxpayers' money to stockpile more salt or have other plans in place to make sure they can get enough grit to keep Britain moving."
Gritting motorways and trunk roads is the responsibility of the Highways Agency in England, Transport Scotland and the three trunk roads agencies in Wales.
Other roads are the responsibility of local government in Britain and the Northern Ireland Roads Service.
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