The cancellation of many routes came after hairline cracks were found in a number of its Hitachi high-speed trains.
A GWR spokesman Dan Panes said cracks were found in the suspension of its Hitachi Class 800 long-distance trains which are now having to be checked.
He said: “We have effectively lost 90 per cent of those trains while Hitachi investigates.
“We are able to release some of them back into service and we’re hoping the situation will improve throughout the day.
“But it will put pressure on those trains that are running so we are advising people not to attempt to travel.
All high-speed GWR services between London, Bristol, Cardiff and Penzance have been cancelled and customers are advised not to attempt to travel today.
Mr Panes said the problems were identified a month ago.
He added that he could not guarantee that normal services would be resumed by Monday.
“We have had around nine trains cleared to go back into service but we would normally have around 50 trains running.
“I would advise commuters not to travel today and to go and get a refund.”
GWR says it will give updates throughout the day.
London North Eastern Railways, which operates the East Coast Mainline, was facing similar problems.
LNER is also advising its customers not to travel today.