It is the latest in a series of closures on the East Coast Main Line for work on signalling systems.
Network Rail said no train services would operate from London up to both Peterborough and Royston, on 31 January and 1 February, as well as 7 and 8 February.
It said services between London and Stevenage via Hertford North would also not operate on those dates.
Meanwhile, on 15 February, Network Rail said there would be no trains between:
Peterborough and London
Potters Bar and St Neots/Letchworth Garden City
Moorgate and Finsbury Park
Stevenage and Hertford North
On 21 and 22 February, trains will once again be suspended between London and Peterborough/Royston, and to Stevenage via Hertford North.
Rail replacement bus services will be in place between Peterborough and Bedford.
As well as signalling work, tracks and crossings are being refurbished, as well as other maintenance.
Ricky Barsby, Network Rail’s head of access integration, said: “A significant amount of vital work is taking place over these four weekends, including further steps to introduce digital signalling to the East Coast Main Line.
Further information is on Network Rail’s website, external.