Services between Brighton and East Croydon are being delayed by up to an hour because of snow in the Purley area.
The runways at Heathrow Airport, in west London, have been cleared overnight and a spokesman said it was "business as usual".
A Gatwick Airport spokesman said 16 incoming flights were diverted to other UK airports due to bad weather and three outgoing flights had been cancelled.
He said: "Flights are being diverted to Manchester, Birmingham and other airports as a result of the weather," adding that passengers are being bussed back to London.
Flights to and from Luton Airport have also been cancelled or diverted. The airport will remain closed until 0700 GMT when the situation will be reviewed.
Driving winds and sub-zero temperatures brought blizzard conditions to much of the UK late on Thursday and in the early hours of Friday.
BBC Weather forecaster Sarah Keith-Lucas said: "We have already seen snow arriving across south-east and north-east England."
She said the worst affected areas in south-east England were Greater London, Medway and parts of Kent, which are seeing "extremely heavy snowfall".
The forecaster said up to 20cm could fall in the worst-hit parts of south-east England and East Anglia, while up to 15cm could fall overnight on the North York Moors and the Pennines.
Snow has caused disruption on some roads. Photo: Rosie Marr.
Met Office severe warnings for heavy snow have also been issued for Yorkshire and Humber.
Up to 20cm (8in) has fallen in some parts of North Yorkshire but there have been no reports of traffic problems.
Some 10cm of snow fell on Thursday night in parts of East Anglia, which made driving treacherous.
The Met Office said the heaviest snowfall overnight was in Norfolk, Bedford and Buckinghamshire.
And a second band is causing severe problems across the Thames Estuary, North Kent and Surrey.
Snow also fell in the Brecon area of mid Wales and in the Neath area of south Wales.
Meanwhile, high winds caused snow drifts to form in parts of Cambridgeshire.
Snow is also forecast in parts of central and northern England, Northern Ireland, Scotland and Wales.
Conditions in the south east of the country are expected to ease during Friday, with more cold and icy weather predicted for Saturday and Sunday.
Further snow is predicted over the weekend, particularly across the north of the UK.
However, the Met Office said it was too early to say whether there would be a white Christmas.
A Met Office spokesman said: "Current indications show an ongoing battle between the colder air currently over the UK and milder air pushing in from the west. As a result the forecast for Christmas Day is still too close to call."
The Highways Agency said it had 94 winter maintenance compounds across England, with 25 in the south-east, and was able to treat all roads within three hours of severe forecasts.
A spokesman told the BBC road users had to "play their part" and "drive appropriately".
"We are asking drivers to carry out simple vehicle checks before they set out; to carry a severe weather emergency kit in their vehicles and to monitor the traffic and weather conditions," he said.
Earlier this week, the AA motoring organisation said half of the UK's local authorities only had enough road salt for six days of continuous freezing.
It said councils had 250,000 tonnes less salt than a decade ago - a claim dismissed as "scaremongering" by the Local Government Association.
Have you been affected by the snowy conditions? Let us know using the form below. You can also send in your snow pictures and video.
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