Train company Southern said it had a number of large trees still blocking lines on the network, which Network Rail was in the process of removing.
The Brighton Mainline has now been cleared of trees, and the first service to run will be the 1019 Brighton to Victoria service, with further services to follow.
Gatwick Express services will be reinstated shortly after this point, and Southern tickets will be accepted on Gatwick Express services.
A statement on the company’s website said: “We will then begin operating on further routes once they have been confirmed as clear, and are safe for us to run services.
“We expect that these routes will include Arun Valley services via Three Bridges.
“Work to clear lines remains ongoing on the East Coastway and other routes, and we hope to have those open as soon as possible.”
Passengers are advised to check www.southernrailway.com before travelling today.