East Coast Trains yesterday was unable to say when normal services would be resumed, although it is understood engineers are working to have tracks cleared by tomorrow morning.
An East Coast spokesman said tickets bought for travel this evening would still be valid tomorrow.
National Rail also said there were major delays between York and Edinburgh.
It said flooding and a landslip caused disruption near Berwick-upon-Tweed, with rising waters leading to delays between Durham and Newcastle.
There were no trains between Durham and Berwick-upon-Tweed, and there was a half-hourly service between Berwick-upon-Tweed and Edinburgh.
Flooding near Haltwhistle in Northumberland meant there were no trains between Hexham, also in Northumberland, and Carlisle in Cumbria.