Most Great Western Main Line trains to and from London Paddington have been cancelled, while London North Eastern Railways is asking passengers not to travel on the East Coast Main Line. TransPennine Express Nova 1 trains had been affected by the issue and were being checked and Hull Trains are also affected.
Hitachi apologised after the issue was found on some of its 800 series trains.
The railway minister Chris Heaton-Harris warned disruption was likely for a "prolonged period".
He said the issue had been found on part of the chassis of some trains on Saturday morning following routine checks.
He said trains would be returned to service as "quickly as possible", but warned that Great Western Railway services in particular were likely to face continued disruption.
He said: "I share the frustration of passengers who are experiencing significant disruption, and would ask people whose journeys are affected to check before travelling."
The minister added he has asked the rail industry to conduct "a rapid and comprehensive review to resolve the issue".
Hitachi said some of its 800 series trains had been taken out of service as a "precautionary measure to allow for thorough investigations", adding it was working to resolve the issue as quickly and safely as possible.
Andrew Barr, CEO of Hitachi Rail, said the decision to withdraw the trains had been taken because of cracks found on the metal that linked the train's body with the underside of the train- known as the bogie.
"We would like to offer our sincerest apologies to passengers for the impact this may be causing for their travel plans."
TransPennine Express and Hull Trains have also been affected by the problem.
Hull Trains said its services would resume as normal following "thorough checks by Hitachi" on its fleet of Class 800 series trains.
However, the operator added that it expected services to be "extremely busy" and could not guarantee that social distancing guidelines would be adhered to.
Passengers have been advised to check train operators' websites before travelling.
"We would like to offer our sincerest apologies to passengers for the impact this may be causing for their travel plans."
TransPennine Express and Hull Trains have also been affected by the problem.
Hull Trains said its services would resume as normal following "thorough checks by Hitachi" on its fleet of Class 800 series trains.
However, the operator added that it expected services to be "extremely busy" and could not guarantee that social distancing guidelines would be adhered to.
Passengers have been advised to check train operators' websites before travelling.
Repairing aluminium trains can be difficult because any of the electronic equipment close to the repair needs to be disconnected and removed and then re-installed after welding repairs have been completed.
Up to 1,000 carriages could be affected by the problem
- The Class 800 is an electric multiple unit - but almost half of them also have diesel engines, enabling them to operate on lines that have not been electrified
- Formal orders for the trains were made in 2012 and 2013 at a cost of around £5.7bn for a 27.5 year programme, including maintenance
- The Class 800 began regular service for Great Western Railway in October 2017 between London to Bristol
- In May 2019, they began service on the East Coast Main Line, with operator LNER branding the train Azuma - or "east" in Japanese
- They were hailed by operators as helping to increase capacity and reduce journey times
- The trains were assembled at Hitachi's plant in Newton Aycliffe in County Durham
Last month, six of the trains were taken out of service by GWR after hairline cracks were found in the suspension system during routine maintenance.
Also see here for a recent posting about Northern Class 195's suffering yaw damper problems