Avanti West Coast said unofficial action by drivers means it is facing “multiple short-notice cancellations” on its network from Monday.
The drivers’ union Aslef strongly denied its members were taking action this week.
Aslef members at Avanti will strike on August 13 as part of the long-running dispute over pay and conditions but the union said nothing else is planned before then.
Avanti said in a statement that cancellations were likely to continue until the current industrial dispute is settled.
“Customers are urged to check their journey on our website before coming to the station, and should be prepared for services to be disrupted at short notice and be very busy.
“We are sorry for the enormous frustration and inconvenience this will cause our customers, and condemn the drivers’ actions.
“We urge them to engage in meaningful talks around modernising working practices and developing a railway fit for the 21st century.”
Mick Whelan, general secretary of Aslef said: “There is no action – official or unofficial – and the company should stop lying to passengers and belittling its staff.”
A union spokesman said the company did not employ enough train drivers to deliver its services.
Aslef members at seven train companies went on strike on Saturday, causing huge disruption across the country.
More strikes are planned in August by Aslef, the Rail, Maritime and Transport union and the Transport Salaried Staffs Association.