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Heavy snow severe weather warning issued for London
A severe weather warning has been issued for Greater London - with up to 10in (25cm) of snow falling.
Heathrow said its runways would not accept arrivals until Monday because of safety concerns in the snow.
Rail operators Southern, Southeastern, South West Trains and London Midland have cancelled some services and are running altered timetables.
Most London Underground lines were delayed after signal point problems caused by the freezing conditions.
The Met Office said heavy snow would affect Greater London on Saturday giving generally 4in to 6in (10cm to 15cm) of fresh lying snow and locally, 9in to 10in (20cm to 25cm).
British Airways earlier advised all passengers on its flights during the affected times on Saturday not to travel to Heathrow, and warned of severe disruption at all London airports.
A Heathrow spokesman apologised for the inconvenience to passengers and said the airport was doing everything it could to make people waiting there "comfortable".
Only the Victoria and Waterloo and City lines are running a good service on the London Underground network.
All other lines are suspended or have delays due to the weather affecting signal points or traction problems on the tracks.
The Bakerloo Line is suspended due to a 24-hour strike by crews at two depots.
Eurostar services are also delayed by up to one hour due to the weather.
The weather has also forced Brent Cross shopping centre in north London to close on one of the busiest shopping days before Christmas.
Heathrow Airport's runways remained shut throughout Saturday
And there are hazardous driving conditions on the M25 between junctions seven and 14 due to snow and ice.
Mayor Boris Johnson said the capital's roads were prepared for more snow.
"Even if it snows 24 hours a day, morning, noon and night for two weeks, we will have enough grit for our roads," Mr Johnson said.
"What I can't guarantee is that [in] some parts of London, if there is heavy snowfall, coupled with ice, bus routes have to be diverted."
Thames Water reported a "near four-fold" increase in burst pipes caused by the sub-zero temperatures.
It has arranged B&B accommodation in London for staff who live outside the capital so they do not have to fight their way through the snow to tackle the problems.