This is following the attempted theft of the rail signalling cables on the line.
Two teenagers in hospital after crashed motorbike sets on fire on Leeds street
Leeds Olympian Nicola Adams and girlfriend Ella Baig reveal baby boy's name as they talk about parenthood
Caught on camera Leeds: West Yorkshire Police need to speak to these people urgently
Met Office storm warning for Leeds - when the stormy weather is due to hit and how long it will last
17 pictures you'll only understand if you're from Leeds
David Horne, managing director at LNER, tweeted:
"My apologies - due to attempted cable theft, LNER services to/from London are severely disrupted today.
"We are only able to operate only one train every hour to/from King’s Cross. Other services will run between Leeds-Peterborough only. Several other services are cancelled."
Tickets valid for today will be accepted for travel tomorrow or Wednesday.
LNER are advising passengers not to travel.