The Met Office had warned of heavy snowfall overnight on Tuesday
Several centimetres of snow have fallen in London and forecasters have warned up to 5cm (2in) more could fall throughout the day.
The Metropolitan Police said the night was quiet with no incidents directly attributable to the snow.
Transport for London (TfL) said it had "well-prepared cold weather plans" following a severe weather warning.
For the most part roads have not been badly affected by the weather but there were problems at Heathrow Aiport.
Some 3cm (1.2in) of snow has fallen at Heathrow where a number of flights were delayed and cancelled. Passengers are advised to contact their airline to check on services.
Four Eurostar services between St Pancras International and Brussels and Paris were cancelled.
Sections of the Northern and Piccadilly Lines were suspended for a time due to the snow.
There were "no incidents" linked to the snow on Tuesday night, police said
However, a subsequent signal failure at Ealing Common led to the suspension of the Piccadilly Line between Acton Town and Rayners Lane, and the District Line from Acton Town to Ealing Broadway.
Services on the Central Line were suspended between Liverpool Street and Leytonstone because of another signal failure, and there were severe delays on the rest of the line.
National Rail Enquiries has set up a dedicated telephone hotline to provide updated information about rail services. The number is 08453 017641.
A Metropolitan Police spokesman said: "There have been absolutely no incidents that we have been made aware of - it's been very quiet.
"There has been nothing that you could relate to the snow."
Tracks at Clapham Junction were turned white (Pic: Chloe Christmas)
Continued light snow is expected in London throughout Wednesday. Pedestrians have been warned that it could turn very slippery.
Temperatures will plummet below freezing overnight, possibly causing the top layer of snow to freeze into ice, BBC London forecasters cautioned.
Mayor of London Boris Johnson said: "The gritters have been in action all over London but if there is a mega dump I would ask people to avoid using cars and check the latest information before leaving home.
"I would also urge Londoners to consider neighbours during this incredible spell of cold weather.
"If you know someone elderly near you who may be struggling it would be most kind-hearted to check they are OK."