The incident is causing problems between Littlehampton, Brighton and Lewes.
A spokesperson for the rail operator said: “The icy weather conditions this morning are causing significant issues across the network.
“As the ice coats the electrical equipment, this stops power from getting to the trains.”
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According to the Met Office, the temperature did drop below freezing between 1am and 4am at Shoreham this morning (October 31).
The 5.44am services from Littlehampton to London Victoria developed a fault just outside of Goring-by-Sea, and was blocking the line between Littlehampton and Brighton.
And the 5.19am Eastbourne to London Victoria was at a stand at Plumpton, blocking the line towards London.
Southern said as a result, the shuttle service between Brighton and Lewes is suspended until further notice.
And services between Lewes and Haywards Heath will divert via Brighton.
The service has now resumed between Brighton and Littlehampton.