More than 40 railway line blockages caused by falling trees have been cleared, but more are expected to be found, Network Rail's managing director of operations, Robin Gisby, has said.
Several hundred Network Rail (NR) staff worked through the night to deal with disruption caused by the severe weather.
Special trains have been used to clear tracks, and Mr Gisby said: " In four cases the train being sent through to inspect the line has hit a fallen tree and we have one train in Devon which is currently disabled following a collision with a fallen tree. We are also dealing with a landslip in the New Forest area."
Mr Gisby added: "As the storm passes from west to east, we will be carrying out safety assessments as quickly as possible to clear routes and get trains running safely.
"We now expect to start services into Waterloo before 9am. Routes from Sussex, Kent and Anglia will follow. Services elsewhere into London are running but at reduced capacity and speed."
Transport for London (TfL) said there was disruption to six Underground lines due to debris from the storm on the tracks.
The Bakerloo, Central, Jubilee, Metropolitan, Northern and Piccadilly lines were all partially closed while workers removed fallen trees and other obstructions, a TfL spokesman said.
North west London, where more of the Tube lines are uncovered, was the area most heavily affected by disruptions.
Overground services were also disrupted, with services not likely to get under way until 9am as TfL scrambled to clear trees from the lines in the north of the capital.