Police have urged motorists to only travel if necessary
Heavy snowfall has caused major disruption on roads in Kent, Surrey and Sussex and closed at least 780 schools.
Every state school in Surrey has been shut and hundreds of others in Kent and Sussex have not opened.
Up to 6in (15cm) of snow fell across south-east England as temperatures plummeted overnight.
Southeastern and Southern trains said they had cancelled their services into London because of the extreme weather conditions.
A Southeastern spokeswoman said: "We are endeavouring to run coastal services in Kent and East Sussex but all trains to London are cancelled."
Southern railway said its services between Brighton and London were cancelled and it was also operating a limited coastal service.
Surrey County Council said it expected all its 403 schools to be closed on Monday and Tuesday.
Up to 220 schools in Kent, mainly in the Medway towns, area of the county, have shut because of the weather.
West Sussex council said 125 schools in the county had not opened on Monday. The majority of schools in East Sussex have also been closed.
The westbound carriageway of the M25, which was shut between junction 8 and 9 in Surrey after several vehicles became stuck in the snow, has been reopened but traffic is slow moving.
A number of sections of the A27 between Lewes and Shoreham were also shut temporarily after vehicles became stranded near Brighton.
Gatwick Airport is open, although services have been disrupted.
Twenty-three flights were cancelled and 18 diverted to other airports when Gatwick closed its runway for two hours on Sunday evening. There is currently no service on the Gatwick Express.
South East Coast Ambulance Service NHS Trust has asked people to only call 999 in an emergency.
It said heavy snow and poor driving conditions meant that its ambulances were taking longer than usual to respond to some calls.
Residents in Surrey have been urged to call police only if there is an emergency.
Your footage of some of the heaviest snow for almost 20 years
Ch Supt Rob Price said: "Surrey Police vehicles are obviously affected by the dangerous, and in some places impassable, road conditions.
"Officers are endeavouring to reach urgent incidents and we are working with partners to ensure an effective emergency service continues to operate despite the severe weather conditions."
Outpatient appointments were cancelled at the Royal Surrey County Hospital in Guildford, Frimley Park Hospital, and Ashford and St Peter's Hospitals NHS Trust.
Rubbish and recycling collections in Tunbridge Wells, Kent, and Horsham in West Sussex were suspended for the day.
The AA has warned motorists to ensure they keep warm clothes in their vehicles if they plan to make a journey, or else risk "flirting with hypothermia".
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