Radio Clyde News said that "at least 30 sets of traffic lights are out across Glasgow after a number of power spikes caused by the bad weather".
Passengers were shut out of some of the country's busiest train stations because of overcrowding and hundreds of thousands of people were left without power.
Britain's transport police, which described the power cut as unprecedented, said officers were asked to help as rail services were suspended and customers on some train lines were being advised not to travel.
Western Power Distribution (WPD), the electricity distribution network operator for the midlands, southwest and Wales, said there was a "major incident".
Large parts of London and the South East are without electricity because of a widespread power cut this evening.
A WPD tweet said: "We are now experiencing a major incident on the national electricity infrastructure".
It later said: "90 percent of customers are now restored and we are working hard to restore the remaining customers as soon as possible". We suspect this has been caused by an electrical supply problem. Ipswich Hospital said it was being affected by the power cut in that area, as its back-up generator had failed to work. One social media user said it was "like GTA out here" as a result.
The Victoria Line on the London Underground were forced to suspend all services.
Meanwhile, separate footage also shows passengers using phone torches for light at Clapham Junction station.
No comment from National Grid was immediately available.
"All trains were stopped while our back-up signalling system started up".