First Great Western cancelled a number of Saturday morning trains including several to London Paddington.
South West Trains said engineers had worked through the night to avoid further delays after Friday's problems.
Lightning strikes and signalling failures had led to a series of cancellations.
First Great Western cancelled 10 services scheduled for Saturday morning because of "poor weather conditions earlier".
It also warned customers further disruption was expected on its services between Paddington and Bristol until 13:30 BST, although all lines have now reopened.
There were delays but no cancellations to afternoon services because of damage to signalling equipment because of the weather.
The company said alterations to its long-distance services should be expected as many of its trains were "not in the correct position".
However, it has pledged to honour tickets held over from cancelled services on Friday for use on Saturday.
On Friday, rail passengers took to social media to complain.
Barry Kirby tweeted: "Paddington is an absolute mess, no real help, limited assistance and a lack of reliable information @fgw - why is it all so fragile?"
Paul Swaddle tweeted: "@FGW commuters understand that there can be problems but utter lack of communication at #paddington is totally unacceptable."
Trains running between London Paddington and Reading, Swindon, Bristol and south Wales were affected by a lightning strike at Twyford, Berkshire, at about 16:00 BST.
A strike in the Surbiton area of south-west London caused problems on services running from London Waterloo to Surrey and Exeter.
BBC weather forecaster Darren Bett said a lot of rain fell in a short space of time on Friday with storms across south-east England causing travel disruption.
The storms later faded away from southern England, south Wales and the south Midlands.
On Saturday, there would be sunny spells in England and Wales while rising temperatures could trigger a few showers, he said.
Areas east of London could see thundery downpours later in the day.
Rail passengers in parts of southern England and Wales are facing further travel problems after stormy weather caused "major disruption" on Friday.