Major routes between Manchester and Birmingham, which passes through Stoke-on-Trent, Coventry and Wolverhampton, along with routes from Leeds to York, Cheltenham to Cardiff and Glasgow to Edinburgh, are all affected.
Services to Plymouth and Penzance are also disrupted with customers relying on Great Western Railway operators as a replacement.
“We are working closely with relevant partners and will provide further updates as soon as possible,” a CrossCountry spokesperson said.
While the operator usually calls at more than 100 stations, it said that the only route expecting a “near-normal” service was between Peterborough, Cambridge and Stansted Airport.
The company apologised to passengers affected and said tickets were being accepted by other operators.
Customers are entitled to Delay Repay compensation if their train is delayed by 30 minutes or more, while those who choose not to travel can claim a refund for their journey.