All services from London Kings Cross to Yorkshire, the North East and Scotland have been cancelled.
Services from Scotland are terminating in York.
Virgin trains services "are virtually suspended" due to the severe weather conditions.
Northern Spirit services to Liverpool are delayed by up to 30 minutes and terminate at Warrington, while the Manchester Airport service is also suffering heavy delays.
Thousands of rail passengers were urged not to travel today after the East Coast network fell into disarray.
All services south of Doncaster were suspended on the East Coast main line due to damage to overhead power lines near Peterborough and flooding on the diversionary route around Hertford.
Spokesman Dave Mallender urged passengers not to travel due to the severe problems the cancellations were causing.
He told the Evening Press:
"We are attempting to run hourly services from Doncaster to Edinburgh, but there is nothing south of Doncaster.
"All GNER services from London Kings Cross to Yorkshire the North East and Scotland have been cancelled until further notice."
Although four buses were on standby to ferry passengers, he said they would not be able to cope with demand and would urge people not to travel.
"We endeavour to run as many trains as possible, but the station is going to be very busy."
Passengers waiting at York were philosophical about the near-total cancellation of this morning's railway services.
Besides helping passengers, GNER staff offered free hot drinks.
This weekend Railtrack undertook its biggest work programme on the network for more than 100 years, prompting widespread delays and cancellations on some services.
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