Trains travelling through Clapham Junction are now running at reduced speeds, with services either delayed by up to 15 minutes or cancelled.
The disruption is affecting services operated by London Overground, South Western Railway and Southern.
Southern said in a statement: “Trains are currently running at reduced speed through the Clapham area.
“This is due to reports of trespassing on the railway.
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“We are unaware at this time when this situation will be resolved.
“If you are already on a train, your journey will take longer than usual.
“Please allow at least an additional 15 minutes to complete your journey.”
National Rail reported the incident at 11.35am on Thursday, June 4.
Passengers are being advised to check journey planners, station boards or the Southern app for live updates before travelling.
Those delayed may be entitled to compensation and are advised to keep their train tickets and make a note of their journeys, as both may be required to support any claim.