Southeastern trains from Orpington to Victoria, Ashford to Victoria and from Sevenoaks to Blackfriars are diverted or delayed as British Transport Police attend the incident.
Train tickets for anyone travelling between Bromley South and Victoria ar being accepted on bus routes. Delays are expected to last until at least 6pm.
Read more: Brace yourselves: Storm Clodagh's here
Elsewhere in London, the Overground has been disrupted and is running with severe delays between Richmond and Stratford due to an object being caught in overhead electric wires at Hackney Central.
Storm Clodagh has brought high winds which could reach up tp 70mph in some parts of England.