Only around ten per cent of Great Western Railway's long-distance services ran over the weekend with similar disruption forecast to take place this week.
The train operator said customers for long-distance services should avoid travelling long-distances if possible and that full refunds would be issued for journeys already booked.
A GWR spokesman said: “Disruption is expected to continue for the rest of the week. Further updates will be provided.”
Local services have been running, but they were expected to be very busy and rail replacement services were limited.
At the weekend, the company said cracks had been detected on "more than one" of its fleet of 93 Hitachi 800 trains, so all were being inspected as a precaution.
GWR was forced to take six of the trains out of service last month after hairline cracks were found in the suspension systems during routine maintenance.
GWR introduced the Hitachi Class 800 high speed trains in October 2017. They are assembled at the Hitachi factory in Newton Aycliffe in County Durham.
Andrew Barr, chief executive officer of Hitachi Rail, apologised to passengers and said the trains were withdrawn because of cracks found on the metal that linked the train's body with the underside of the train, known as the bogie.
The UK government has asked Hitachi to set out a comprehensive plan to identify the extent of the cracking and outline a longer-term repair strategy.
Robert Nisbet, of the Rail Delivery Group, said 183 high speed trains taken out of service on Saturday had been inspected by Sunday evening but warned that disruption was expected to "carry on for a few days."
The problems with the trains are also affecting other train operators, including London North Eastern Railway and Hull Trains.
GWR is urging passengers to check services before booking. Commuters can use their tickets on the following services:
• Avanti West Coast trains between Birmingham New Street and London Euston
• London Northwestern Railway trains between Birmingham New Street and London Euston
• West Midlands Railway trains between Hereford/Worcester and Birmingham New Street
• Chiltern Railways via any "reasonable" route
• CrossCountry via any "reasonable" route