A map suggested parts of Devon, Somerset, Gloucestershire, Dorset and south Wales will be among the most affected.
Commuters in many parts of the country were warned to leave work early on Thursday to ensure they got home.
Forecasters have predicted ice and snow which could lead hard driving conditions and disruption to transport services.
Meanwhile, temperatures have fallen to the lowest level this winter, with Braemar, Aberdeenshire, dropping to -14.4C (6F) this morning.
From about 7pm there is a chance of light snow across the county but the Met Office has warned by 8pm there is a 90 per cent chance of "heavy snow" which could continue to fall for the next few hours.
On Thursday morning, Southeastern Trains said 21 trains were cancelled or altered to minimise the impact of ice forming on the rails.
The Met Office upgraded its warning today as it said that cancellations and delays to rail and bus journeys are likely, while some vehicles could be stranded and rural communities cut off in the worst cases.
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Further snow was forecast today with 5-10cm expected in Wales and the southwest.
Wilson said the cold temperatures were due to stick around for the foreseeable future.
"Saturday is looking like a pretty decent day if a rather cold one", she said.
Coastal areas may also see the odd wintry shower, with a maximum temperature 2C.
It should become drier and maybe brighter by the afternoon, feeling very cold in strong northeasterly winds.
Bookmaker Ladbrokes has slashed odds on this winter proving to be the coldest on record.
Ladbrokes spokesman Alex Apati said: "Extreme conditions are set to batter Britain and we've slashed odds on this winter being a record-breaker as a result".