Passengers were urged to avoid travelling on the East Coast Main Line on Monday after heavy rain flooded several stretches of the network.
Forecasters have warned of more rain in the next 24 hours
GNER services between Leeds and London were suspended and there was disruption between England and Scotland.
Tickets bought on Monday will be valid on Tuesday, said the firm.
In addition to the flooding, rainwater leaked into signal boxes and there was an overhead line problem at King's Cross, according to Network Rail.
Speaking on Monday, a company spokeswoman said: "Severe weather being experienced in Yorkshire is causing major disruption on all transport - including the railways.
"We are working closely with our partners in the train operating companies to run as many services as is safely possible but widespread flooding has caused many delays and cancellations."
Anyone who is planning to travel should check with National Rail Enquiries before doing so, she added.
High winds and heavy rain caused chaos for thousands of travellers across England, and severe weather warnings were in place across most of the country.
On Monday, GNER spokesman Alan Hyde said: "Passengers should not travel unless absolutely necessary. If journeys can be deferred until the bad weather has cleared then there will be much less disruption.
"There's flooding in a number of areas and for the moment we're just hoping that the wind and heavy rain will abate."