Rail firms have been told to find extra trains by the Government amid fears delays caused by the cracks discovered in some carriages could last throughout the week.
Travellers were beset by delays and cancellations throughout the weekend after Hitachi 800 trains were pulled from the lines on Saturday morning as a “precautionary measure” after a fault was found in some trains.
Great Western Railway (GWR) and London North Eastern Railway (LNER) advised people not to travel today, while those due to travel with LNER tomorrow have been advised to check travel information before heading to the station.
The fault relates to cracks found on the metal that links the body of the carriage with its underside, although it is not understood to be a risk to passengers.
Chris Heaton-Harris, the rail minister, said rail firms should urgently set out a plan for safely restoring services as soon as possible.
He also said Hitachi needed to provide details of its plans to identify the extent of the cracking issues and their safety.
He added: “I expect operators to explore all options for replacement services to help people complete their journeys, and have asked Hitachi for a safety inspection plan, as well as a longer term repair strategy.
“Our focus is to ensure trains are returned to service as quickly as possible, once they are fully approved as safe. Only then can we start to rebuild a reliable and punctual timetable for passengers.
“I also want to thank passengers for their patience during what could be a significant period of prolonged disruption, likely to continue for some time.”
The Government also said the rail industry should set out a plan for managing capacity by moving rolling stock and proposing where alternative trains can be sourced, as well as a clear rail replacement schedule.
Speaking on BBC Breakfast earlier today, Robert Nisbet, regional director of the Rail Delivery Group, which represents rail operators, said disruption would be expected to continue into the coming week.
“With the inspections completed initially by the end of today, we are still expecting some disruption to carry on for a few days,” he said.
"It's impossible for me to say exactly how long that is going to take, but we are obviously going through this as quickly as possible, but we don't want to rush it.”
Mr Nisbet said: "It's fair to say this didn't pose any particular danger to passengers that were travelling on those trains but if you don't treat these kind of issues early on then they have the potential to develop."
On Saturday Hitachi apologised for the disruption and said that by that evening some of the trains would be back in use after being cleared to run as normal.
The first stage of investigations is now understood to be complete, with the next involving more technical checks which will help determine the route forward.
It is unclear how many trains will need to be repaired.
A spokesman for Hitachi said: "Safety is our number one priority and as a precaution, the decision was taken to halt the entry into service of our intercity fleets pending inspection.
"We understand the frustration caused and we would like to apologise for the inconvenience caused to passengers and operators.
"Having been cleared for service, some trains are now running again across the network."
A spokesperson for the Rail Delivery Group, said: "While services are back up and running on many of the affected routes, in those areas still impacted companies are working together to consider all options for getting people moving again.
"In the short term, this includes passengers being able to use their tickets on other operators’ trains and in the medium term potentially using alternative rolling stock.
"Should it be necessary to use different trains, this will be done as quickly as possible taking into account the need for safety checks. We apologise for the inconvenience we know this will be causing passengers on the routes affected and people should apply for refunds where appropriate."
Passengers who were unable to travel at the weekend can use their tickets on services throughout the week while those who choose not to travel can claim a refund.
The RDG said this should continue for as long as the disruption lasts but advised passengers to check with individual rail firms for their policies.
Anna Celac, an Instagram photographer, told the BBC she had to cancel a trip from Cardiff to London to see a friend for the first time in more than a year. She said she had been disappointed to cancel but the rail replacement bus would not have left her with any time in the City.
Rail firms are not understood to be able to call on old stock to fill the gaps in service as it would need to be modernised to meet current standards and may require special permission to be put back into use.
The old carriages and engines would also need to be inspected to ensure they were still operational.
A source at one rail firm said it was considering shifting unaffected trains onto different routes they do not normally run on in order to restore services.
The Hitachi trains are also being returned to the tracks once they have been checked and passed for use.