A replacement coach service will connect passengers with other trains
Virgin has accused Network Rail of breaking its licence agreement by closing part of the West Coast mainline near Rugby at short notice.
An estimated 60,000 passengers expected to use the line on New Year's Eve face an extra hour on their journey times.
Network Rail has apologised but insists key work must be done over the festive period when passenger numbers are down.
The line was due to be closed on 27 December for three days but Network Rail added an extra day of work, which is part of the £8bn upgrade of the line.
The Office of Rail Regulation said it is investigating the complaint but ruled the work must go ahead.
Shadow transport secretary Theresa Villiers said: "Scheduling track works on December 31 is misguided and Network Rail should think again about this decision and the inconvenience it will cause for passengers."
Network Rail is extremely sorry and apologises to passengers for the inconvenience
Network Rail spokesman
The latest disruption will affect mainly Virgin Trains to and from the West Midlands, north Wales, north-west England and Scotland.
A coach service will replace trains between Northampton and Birmingham International.
Some London Midland and First ScotRail Sleeper services that would have passed through Rugby will also be affected.
Anthony Smith, chief executive of Passenger Focus said: "This is unbelievable. Thousands of passengers have booked or planned New Year travel in good faith.
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"We feel very let down and want re-assurances that the huge amount of engineering work planned for next year will not run into similar problems."
Up to 60,000 travellers are expected to use the line on New Year's Eve and Virgin has warned them in a series of newspaper adverts to add at least an hour to journey times.
A message on its website guarantees that every passenger will get to their destinations in time to celebrate the New Year.
Chris Gibb, managing director of Virgin Trains, said: "I am extremely disappointed that Network Rail have informed us of this new disruption at such short notice. Network Rail have insisted this work goes ahead on this crucial travel day."
'Key work'
The engineering work is part of a major overhaul of the West Coast Main Line which began in the mid-90s.
A Network Rail spokesman said: "Work will be ongoing for most of the next year, but the Christmas period is the last major opportunity we have to do key work while passenger numbers are down during the relatively long holiday period."
He added: "It was only realised at the beginning of December that work was falling behind. Rail companies are usually given 12 weeks notice of engineering work. Virgin were told only at the beginning of the month, so that is very late.
"Network Rail is extremely sorry and apologises to passengers for the inconvenience."
Virgin Trains Pendolino on the West Coast Main Line; Virgin will be worst affected by the closure.
The Office of Rail Regulation (ORR), the regulatory authority for Great Britain's railway network, has launched an investigation of Network Rail procedures following a complaint from Virgin Trains regarding over-running engineering works on New Year's Eve. 

Network Rail, who are responsible for the British railway infrastructure, have announced that as part of ongoing engineering work to improve the West Coast Main Line, no services will be able to pass through Rugby on December 31. 

The closure will affect services operated by Virgin Trains, London Midland and First ScotRail.

Chris Gibb, the Managing Director of Virgin Trains said, "I am very disappointed that Network Rail (NR) has given us so little opportunity to warn our passengers of this further disruption. We were first warned of the possibility of this additional work on 6 December."

"Because of the seriousness of the situation we felt it necessary to refer the matter to the Office of Rail Regulation. We simply cannot have NR bullying train operators in this way just because their engineering planning processes are in a mess."

The company has warned passengers that journeys are likely to be extended by an hour or more in some cases. 

Whilst the ORR will be investigating the complaint from Virgin, they have ruled that the work should still go ahead. 

A spokesman for Network Rail said, "Work will be ongoing for most of the next year, but the Christmas period is the last major opportunity we have to do key work while passenger numbers are down during the relatively long holiday period.

"It was only realised at the beginning of December that work was falling behind. Rail companies are usually given 12 weeks notice of engineering work. Virgin were told only at the beginning of the month, so that is very late.

"Network Rail is extremely sorry and apologises to passengers for the inconvenience."

According to the company, the engineering works will contribute to enabling increases in service frequencies and reductions in journey times on the West Coast Main Line from December 2008.