It comes after lines were blocked between Lockerbie and Carstairs in Scotland due to damage to overhead electric cables.
In addition, a freight train has broken down at a platform in Carlisle.
Avanti West Coast says customers should not travel on services southbound from Edinburgh or Glasgow Central to London Euston.
It also urges customers against travelling north of Carlisle.
A second operator, TransPennine Express, has also issued a “do not travel” warning north of Carlisle.
There are no trains between Carlisle and Glasgow Central or Edinburgh in both directions and there are no replacement buses.
National Rail warns that “major disruption is expected until the end of the day”.
