Network Rail has urged passengers not to travel to and from London on the East Coast Main Line on January 25 and 26 as well as February 29 and March 1, as no trains will be calling at King's Cross.
In addition, there will be five weekends where services on the southern section of the route - which stops in Leeds, Wakefield and Doncaster - will be reduced.
Trains running on January 4 and 5, January 11 and 12, January 18 and 19, February 8 and 9 and February 15 and 16 will be very busy and passengers are advised to allow extra time for their journeys. The weekends of February 1 and 2 and February 22 and 23 will see a normal service.
Network Rail's decision to close the East Coast Main Line to London over the August Bank Holiday this summer - meaning it coincided with the Ashes Test at Headingley, York’s Ebor Festival and rugby league’s Challenge Cup final - was heavily criticised.
Further disruption is planned from March onwards, and there will be no services on Christmas Day and Boxing Day, then a reduced service at King’s Cross on Friday December 27.
The agency responsible for the nation's rail infrastructure says the work being carried out on the two weekends next year "can only be carried out safely when no trains are running on this section of the railway".
This includes upgrading the power supply and overhead line equipment in and around King's Cross station as well as building an extra platform and installing new track at Stevenage station.
The East Coast Main Line carries over 20 million passengers every year and links London to Edinburgh via Peterborough, York and Newcastle. Network Rail says the upgrade "is the biggest improvement into the line in a generation and will bring widespread and long-lasting benefits for passengers", including more frequent services and an extra 10,000 seats a day for travellers.
Ed Akers, Principal Programme Sponsor for Network Rail, said: “Firstly, we would like to thank passengers for their patience so far and ask them to bear with us while the next stages of work take place.
“We’re really sorry for the disruption this work will cause, but the East Coast Main Line is long overdue an upgrade. We’re working to provide more seats and more frequent, reliable and faster journeys for the millions of people who use the line every year – and we can’t do that without causing some disruption.
“We’re doing our very best to keep passengers moving while the work is underway, but anyone using the line at weekends over the next couple of months should check before travelling.”
Services on the East Coast Main Line have been brought back under public control following the failure of the Virgin Trains East Coast franchise.