Hitachi 800 trains were stopped in their tracks on Saturday and Sunday after the fault was discovered.
Great Western Railway and London North Eastern Railway have advised people not to travel today, and announced more cancellations are expected across this week.
A spokesperson for GWR said: “A number of 800 Class Hitachi trains have been withdrawn from service for precautionary safety checks.
“As a result a significant number of long-distance services will be cancelled on Monday 10 May and disruption is expected to continue into the following week.”
There are no services, or only an extremely limited service on these routes:
London Paddington, calling at Swindon, Bath Spa, and Bristol Temple Meads.