Rail engineering work which was already over-running has been extended by another day and will now affect some trains on New Year's Day.
Replacement bus services are in place
Network Rail said it was "extremely sorry" the West Coast Mainline had to be shut at Rugby, Warwickshire.
The work will now affect Virgin Trains to and from the West Midlands, Scotland, north Wales and north-west England until 0530 GMT on 2 January.
Some London Midland and First ScotRail services will also be affected.
Buses will replace trains on the 40-mile stretch between Birmingham International and Nuneaton, adding up to an hour to journeys.
Chiltern Railways, which operates services between Birmingham Snow Hill and London Marylebone, said it would honour all tickets from West Midlands' stations to London, no matter which firm issued them.
However, it said that with the additional passengers services are likely to be very busy.
Services had been due to return to normal on 1 January, but on New Year's Eve, Network Rail announced that work was still not complete.
A spokesman for the company told the BBC News website: "We have put in all the extra resources that we possibly could, but things just haven't gone as well as we hoped."
Network Rail said that as passenger numbers were lower over the festive period it was essential to carry out a large part of the £8bn upgrade of the line then.
Up to 60,000 travellers had been expected to use the line on New Year's Eve, and Virgin had warned them in a series of newspaper adverts to add at least an hour to journey times.
Virgin has complained that Network Rail did not give it enough notice.
The rail regulator is investigating its complaint.
Earlier Dr Claire Wells, of the Rugby Rail Users Group, said Network Rail's planning should have been better.
"Either they should have had this closure in their scheduling from the start or they should have worked through so they did not need this additional day."
Shadow transport minister Theresa Villiers also said she was disappointed to hear about the New Year's Eve disruption.
She said: "I'm astonished that Network Rail have done this - New Year's Eve is a time when we really want to see people on public transport and not in their cars.
"Suddenly they are saying that they are closing off important swathes of the track - that's going to cause a lot of hassle for passengers and frankly they should have done a better job in getting their engineering works finished on time."
Commuter Alan Crosby, from Coventry, said he had been forced to work from home on New Year's Eve.
He said: "It's really frustrating as I expected things to be OK today but found out at short notice that the line was closed.
"There appears to be no consideration for people that work in between Christmas and New Year on the non-holiday days."
Sina Cohen, from Warwickshire, said: "I was at the railway station and couldn't believe my eyes when I saw the notice explaining how I have to miss New Year's Eve in Scotland with my son and his gran.
"Network Rail need a reality check."
You can read a selection of readers' comments below:
This has been going on for ages. At the moment you can't travel between Stratford and Liverpool Street; Chelmsford and Shenfield; Stratford and Enfield and they are the ones I know. Rail travel is dismal that's why people use cars.
Marie P, Romford
I'm shocked that Network Rail justify this disruption by suggesting passenger numbers are lower over the festive period. I travelled from Reading to Birmingham on Virgin trains yesterday. The train was dangerously full, with most of us having to stand in already overcrowded aisles. As a seasoned commuter myself I am used to a bit of overcrowding, but it's the last thing I expect mid-morning on a Sunday in late December. I'm sure the people making these decisions are unlikely to see their incompetence first hand.
Three of us came down in the car yesterday a day earlier to avoid this mess. I'm glad we did as the roads were ordinarily quiet for a Sunday. It's beyond belief that Network Rail cannot put this back a mere 24 hours.
Ian Upton, England
The situation has been hopeless - but there is nothing the workers can do to change things. It is not just this week, but the rail service has been declining fast over the past five years. The statistics are skewed to make things look better than they really are.
James Millar, Essex, England
I had planned to go down to the west midlands to visit my great uncle as it's his 101st birthday. My plans were tough as it was due to my remote location, it involved 2 trains to Glasgow then a Virgin train down south. However this additional time to add on means i will miss a considerable part of my great uncle fred's party. Some compensation must be paid for inconvenience.
Richard Kennedy, Uddingstone, near Glasgow, Scotland
Having spent 6 hours travelling the 100 miles between Blackpool & Sheffield on Thursday 27 Dec, I am still VERY angry about this and have all the sympathy in the world for people who are affected by this. It's apparent that the people in charge of Network Rail could not run a bath let alone a Rail Network.
Jamie Bell, Sheffield, England