Train lines have re-opened since the incident on Tuesday afternoon but trains may be cancelled, delayed or revised, rail chiefs warned.
The disruption is expected to last until the end of Tuesday.
In a statement on its website, South Western Railway said: “Following a person being struck by a train between Surbiton and Clapham Junction all lines have reopened.
"However, as services are severely delayed due to crew displacement customers are advised to travel later if possible or consider delaying non-urgent travel while service recovery is ongoing."
Network Rail said lines have reopened between Woking, Sutton and Wimbledon following a person being struck by a train.
"Trains may still be delayed by up to 30 minutes or cancelled whilst service recovers," Network Rail said.
Affected travellers can use their tickets at no extra cost on other services including the London Underground, Overground, Thameslink, Southern, Great Western Railway and CrossCountry.
In addition tickets will be accepted on all TFL bus routes between Surbiton and Wimbledon.