National Rail said travellers should plan for services to be cancelled.
It said the issue appears to be a fault with the onboard GSMR radio system, which is used to communicate in case of emergencies.
According to the Rail Safety and Standards Board Rule Book, in the case of a radio system failure, trains cannot exceed 100mph (160km/h), or 60mph (100km/h) through affected areas.
National Rail said it is investigating the cause of the fault.
Delays of around 10-15 minutes are expected on Southern, Thameslink and Great Northern services, with some short notice cancellations possible.
Most passengers on these lines will be able to travel on their normal route, National Rail has said. Disruption is currently expected to continue until 12:00 GMT.
The Gatwick Express is only running between London Victoria and Gatwick Airport, not serving Brighton.
Elizabeth line services between Reading and Heathrow Airport are also affected.
ScotRail says its services were impacted earlier this morning but are no operating normally.
GSMR works in a similar way to mobile phones, but the digital system is not reliant on commercial mobile phone operators. The rail network has its own contained phone and mast system.
One rail source told the BBC that “the system isn’t connecting easily”.
There is a work around that staff can use, but it takes time to implement.