Southern Rail made the announcement just before 5 p.m.
This is a small tree partly on the track before the London Road Viaduct.
A Southern Rail spokesman said: “Network Rail is on site and confirms it will take approximately 30 minutes to switch off the power and remove the tree.
“The line to Brighton will be blocked at this time.”
The Met Office has issued a yellow warning for thunderstorms in effect between 4am today and 2am tomorrow.
Just before 5:00 p.m., it was windy and raining.
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