Some lying snow could reach up to 10cm or more over higher ground and ice is expected to form on untreated surfaces.
Southern Rail said overrunning engineering works at South Croydon will affect early morning trains between East Croydon and Uckfield/East Grinstead.
In a post on X, the Met Office said roads were expected to be icy, and advised people to take extra care when travelling.
Tuesday saw widespread snowfall, with 12cm of lying snow recorded at Watnall, Nottinghamshire, as an Arctic airmass influenced the UK’s weather.
The Met Office said the coldest temperature was recorded at Braemar village in Aberdeenshire, Scotland, with the mercury falling to minus 11.2C on Tuesday.
Thousands of train passengers suffered disruption on Tuesday morning and a Stagecoach bus in Aberdeenshire toppled onto its side with a passenger on board in icy conditions.
The UK Health Security Agency (UKHSA) has issued the first amber cold weather health alert of the season, warning conditions could be dangerous for vulnerable people, including the elderly.
The amber warning covers the east and north of England, the Midlands, and Yorkshire and the Humber, with yellow alerts coming into place for the South East, South West and London until 6pm on Saturday.
Met Office chief meteorologist Neil Armstrong said: “With cold Arctic air firmly in place over the UK, continued winter hazards are likely through much of this week, with further updates to warnings likely in the coming days.”