However, the company says there are likely to be restrictions on the line between Ealing Broadway and London Paddington which will limit the use of electric trains in the evening rush hour.
Class 802s, a variant of the Intercity Express, have already entered passenger service on GWR between London, Plymouth and Penzance, while another test train ran successfully to Newquay on Monday, in preparation for the withdrawal of all full-length HSTs on GWR.
Network Rail is still advising you check before you travel, as there may still be some delays.
In a statement this evening, Network Rail warned that not all of its repairs could be completed over night.
South Western Railway, Chiltern Railways, Virgin Trains, West Midlands Railway and Transport for Wales are all accepting GWR tickets, while tickets for GWR services today will also be valid tomorrow.
Two of the four lines from Paddington were opened at about 12.40pm on Wednesday after engineers cleared debris and restored power so trapped trains could be moved.
Passengers have been urged not to attempt to travel via London Paddington this morning, after a major power failure left some trains stranded on the tracks for hours.
Class 802 trains are bi-mode, meaning they can operate on electric and diesel power.
Travellers trying to get to Heathrow were told to take the much slower Piccadilly Tube line to the airport or a bus replacement service.
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.
Commuters across London faced serious difficulty getting to work this morning as services faced extreme difficulty.
Matthew Benjamin tweeted about chaotic scenes at Reading, and said he'd had to queue in an underground vehicle park for a taxi to get back to London, where he had two night buses ahead of him.
Saudi Royal Family Admits Jamal Khashoggi Has Died
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When the wind blows, Antarctic's ice shelf 'sings'
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Brewers Pull Wade Miley After Five Pitches
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