Firefighters worked on the blaze for almost three hours, eventually extinguishing it at 04:30 BST. No injuries were reported in the incident.
Later in the morning, storms brought more than an inch of rain to parts of Wales and the Midlands in just an hour.
Parts of Wales and central and southern England could see further thunderstorms on both Sunday and bank holiday Monday, with the Met Office warning of the possibility of power cuts and delays to trains and buses.
Many people got out their cameras to photograph and video Saturday night's electrical storm, which was called "utterly insane" and "like being under a strobe light".
Others remarked that they had "never seen a storm quite like this" and said the flashes were "stunning".
BBC Weather presenter Tomasz Schafernaker called it the "mother of all thunderstorms" as he watched it over London.
"I've never seen a storm with such frequent lightning in my life I don't think. Mostly sheet lightning and not too loud but flashes are spectacular," he said.
Forecaster Gemma Plumb, from BBC Weather, said that as the storms pushed northwards across England on Sunday, more would be coming up over the English Channel from the continent.
The Met Office weather warning for rain is in force until 06:00 on Monday and covers all of Wales as well as southern and central England.
Flooding of homes and businesses could happen quickly, the Met Office said. It added that fast-flowing or deep floodwater was possible with damage to some buildings from flooding, lightning strikes, hail or strong winds.