Southern says some of its services could be disrupted in the South East until about midday, including a “very reduced” service between Portsmouth and Barnham in West Sussex until after 10:00.
The train operator said there would also only be an hourly service between Epsom Downs and London Victoria until after 10:00, and between Uckfield and London Bridge during the morning.
South Western Railway said due to a precarious tree at Frimley, trains were running at reduced speed on the line towards Ascot.
Services across the network have been starting later than usual due to safety inspections, and trains are running at reduced speed on all lines, South Western Railway says.
There were delays on DFDS Seaways between Dover and Calais and between Dover and Dunkerque due to strong winds in the Channel, the operator said, but these have now eased.