Network Rail engineers are working to fix the damaged lines and to recover stranded trains, and hope to have two of the four lines working again by midday.
A Network Rail spokesperson said: "Extensive damage to 500 metres of overhead electric power lines last night means no trains have been able to run between London Paddington and Reading and Heathrow this morning".
GWR said because one line remained closed "some alterations will be experienced on commuter services in the Thames Valley, particularly trains serving the stations of Maidenhead and Twyford".
It said GWR tickets were still being accepted from Waterloo, Marylebone and Euston for travel on South Western Railway, Chiltern Railway, Virgin Trains, West Midlands Railway and TfW rail.
The disruption affected passengers as far as south-west Wales, Bristol, Exeter, Plymouth and Penzance, according to Great Western Railway. The train was not in passenger use.
Class 802 trains are bi-mode, meaning they can operate on electric and diesel power.
Trains to London's Heathrow Airport were among those affected, though by mid-afternoon a limited service had resumed.
GWR is investing £500m in the new fleet delivered by Hitachi which will replace the operator's high-speed rolling stock by the end of next year.
This morning's issues come after commuters faced major delays on Tuesday evening as electricity supply problems caused delays and cancellations on a number of busy routes in and out of London.
Great Western Railway has urged people to "only travel if necessary".
Matthew Benjamin tweeted about chaotic scenes at Reading, and said he'd had to queue in an underground auto park for a taxi to get back to London, where he had two night buses ahead of him.
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