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.

The suspect, who was shot dead by police, has not been identified.
Officials say he was a disgruntled lawyer who fired randomly at drivers.
Numerous weapons were found in what is believed to be the suspect's car, Houston's acting police chief said, adding there were no indications of anyone else being involved.
Police say they are also investigating the gunman's apartment and his social media accounts to try and establish a motive.
"The motivation appears to be a lawyer whose relationship with his law firm went bad,", Houston Mayor Sylvester Turner told reporters.
Six victims were taken to hospital, and three were treated at the scene after being shot at while inside their cars, the city's acting Police Chief Martha Montalvo said. One of the victims is in a critical condition.
The shooting comes three days after a shooting at a shopping mall in Washington state, in which five people were killed.
The gunman in that attack, Arcan Cetin, 20, was born in Turkey and is a legal US permanent resident, officials say.
The FBI have said there was no evidence that the shooting there was linked to terrorism.
Nine days ago, a 20-year-old man stabbed 10 people at a Minnesota shopping centre before being shot dead by an off-duty police officer.
Rail passengers in parts of southern England and Wales are facing further travel problems after stormy weather caused "major disruption" on Friday.
[NEXT_CONCEPT]
Nine people have been injured in a shooting outside a shopping centre in Houston in the US state of Texas, one of them critically.