There are currently no train services between Eastbourne – Hastings and Eastbourne – Ashford International.
This is due to fallen trees on the tracks.
Storm Bella is the second period of severe weather to be officially named by the UK’s Met Office this winter.
Communities Secretary Robert Jenrick urged people to check official advice, including from the Environment Agency, which asked people to keep away from “swollen rivers and flooded land”.
A statement on its website said: “It is often deeper than it looks and just 30cm of flowing water is enough to float your car.”