Network Rail, said all Great Western Railway (GWR) trains between Paddington and Slough had been cancelled until at least midday after overhead electric cables were damaged at Ealing on Tuesday night.
Trains between Paddington and Heathrow airport are also not running.
Services are likely to be affected all day, Network Rail said.
There were also major delays for commuters using Victoria Station on Tuesday evening after an electricity supply failure.
GWR said damage to the overhead wires had left many trains stranded on the line between Paddington and Reading.
“Owing to the extent of the damage, no trains are expected to be able to operate between London Paddington and Hayes & Harlington in either direction for much of Wednesday,” the operator said.
“As a result, GWR, TfL Rail and Heathrow Express will not be operating a train service between London Paddington, Hayes & Harlington or Slough until such time as repairs have been completed.”
South Western Railway warned customers their trains into London would be “very busy” as a result of more people using their services.
Network Rail said it was “working to recover all the stranded trains and to rectify the damage to the overhead electric wires”.
It said it hoped to reopen two of the four affected lines from midday, but GWR advised passengers not to attempt to travel between Paddington and Slough until at least 12:00 BST.
Network Rail issued advice on alternative routes for passengers affected including a replacement bus service for those heading to Heathrow.
TfL Rail services are suspended until at least 14:00, Network Rail said.
‘I should have stayed in bed’
One commuter said his alternative route to get to a meeting in Bristol would add an hour and a half to his journey time.
“They told me as an alternative route I’ll have to go from here to Waterloo, from Waterloo to Reading, and from Reading then to Parkway,” he told.
“It’s not convenient, but we have no other option,” he said.
Sam Haworth, from Reading, said he would about an hour and a half late for work.
The 32-year-old added: “Before I arrived at the station I didn’t know there were issues. I should have stayed in bed.”>