Lord Hendy told MPs that Department for Transport (DfT) officials will continue to examine the issue throughout the festive period.
Many train drivers and other crew members do not have Sunday working included in their contracts, with numerous operators often relying on them volunteering to work extra paid shifts to run timetabled services on that day.
This regularly causes the cancellation of hundreds of trains across Britain, such as on Father’s Day or the day of a major England football match.
Giving evidence to the Commons’ Transport Select Committee, Lord Hendy said the Government is worried about “staffing of Christmas services”.
“That we are concerned about with several train operators, exacerbated by the fact that inevitably the closures close parts of the railway and put more pressure on others.”
He added: “I’ve been through this a lot with Alex (Alex Hynes, director general for the DfT’s rail services group) recently and will continue to be into, right up to and over Christmas.”
Mr Hynes said: “Generally as a system, we’re over-reliant on overtime working for train crew.
“That’s a risk, which may be worse at Christmas time than other times.”
Britain’s rail network completely shuts down every year on Christmas Day, with a limited service on Boxing Day.
Many routes will be closed for longer during the festive period because of Network Rail carrying out engineering work.
Lord Hendy, who chaired Network Rail from 2015 until he was brought into the Labour Government, said: “Christmas is a good time to do major engineering work, because the demand is lower over several days.”
Network Rail has previously said passenger numbers at major stations typically drop by 50-60% during the seven days between Christmas Day and a new year compared with a week in November or early December.
Lord Hendy explained that finishing engineering work on time is vital, as he recalled Christmas 2014 when the reopening of London King’s Cross station was delayed, causing chaotic scenes at Finsbury Park station.
He said: “The lessons of that were very severe, and the rail industry and Network Rail, in particular, has worked extraordinarily hard not to replicate that again, because it was disastrous, and disastrous for passengers.”
London Liverpool Street station will be closed from Christmas Day until January 2 because of renewal work at Bishopsgate Tunnel and improvements to the passenger experience.
Travellers are advised to use Victoria line Tube services from Walthamstow Central or Seven Sisters.
No trains will call at London Paddington between December 27 and 29 because of preparatory work necessary for HS2’s Old Oak Common station.
That means Heathrow Express trains will be unable to run between Paddington and the west London airport.
Some Great Western Railway services will be diverted to or from Euston, but the majority will stop or start at Reading or Ealing Broadway.
Signalling work in the Crewe area between Christmas Day and January 2 will cause significant changes to services, with no trains passing through Crewe station on December 27.
There will be no direct services between Crewe and Liverpool, and a reduced service between Crewe and Manchester, from December 28 until January 3.
Services in the Cambridge area will be disrupted between December 27 and January 5, affecting CrossCountry, Greater Anglia, Great Northern and Thameslink.
