“Northern, Network Rail and all other affected train operators are currently in the process of moving stranded trains that have been impacted by this incident,” it added.
“Once this has taken place we will work to recover the timetable.”
A BTP spokesperson said officers were called to the line near Levenshulme station at about 14:00 to reports of “a person in a precarious position”.
“Officers attended alongside Greater Manchester Police, paramedics and fire and rescue, and a person was arrested in connection [with the incident].”
Services affected cover several areas across the North West, as well as trains between Carlisle and Newcastle, and parts of Teesside and Yorkshire.
Other train operators affected included Avanti West Coast, CrossCountry, East Midlands Railway, Northern, TransPennine Express and Transport for Wales, National Rail said.
A Northern spokesperson said: “All other services in the North West will be at risk of cancellation and disruption due to the severe impact caused by this incident.
“Customers with tickets to travel on Northern services can travel on board Manchester Metrolink Tram Services, TransPennine Express, East Midlands Railway, Transport for Wales & Cross Country services via any reasonable route until the end of the day.
“This will be the quickest route to/from Manchester City Centre – Manchester Airport.”
