Update at 4.45pm: Network Rail says it has repaired some of the damaged signalling system caused by a lightning strike between Oxted and Uckfield, but not between Crowborough and Uckfield.
It says services twoards Uckfield will terminate at Crowborough and services from Uckfield will start at Crowborough.
Network Rail says Southern will not be able to operate a full peak service this evening because of being unable to terminate and restart two services an hour at Crowborough.
There are buses operating between Haywards and Heath and Uckfield via Crowborough.
From our story published earlier today: Trains running between Uckfield and London Bridge have been suspended following a lightning strike.
Southern announced the problem on Twitter at 11:04 and their website shows all trains cancelled until 13:52.
Further tweets from Southern say the line is blocked between Oxted and Uckfield due to a signalling fault.
National Rail, who own and maintain the equipment, say they have staff attending to effect repairs. They expect disruption until 2pm.
Buses are running between Oxted and Uckfield and arrangements have been made for tickets to be accepted on Brighton and Hove buses between Uckfield and Tunbridge; Seaford & District between Crowborough, Tunbridge Wells and Lewes, and Southeastern between London and Tonbridge.