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London Fire Brigade took a day's worth of calls in 90 minutes, with its crews attending flooded premises and roads, and properties hit by lightning.
A Met Office amber "be prepared" warning has been issued, and there were reports of 40mm of rain in some areas.
The Environment Agency has four flood warnings in place.
Rivers in Bromley and Sidcup in south-east London, and Basildon, Essex, are affected.
Meanwhile, Abellio Greater Anglia, South West Trains and Southern have warned of major delays on some rail routes.
And in London parts of the Tube and Overground railway have been suspended because of flooding.
On Twitter, Transport for London posted incidents of localised flooding on roads, including the Blackwall Tunnel in the east of London, which was temporarily closed.
The Met Office said the rain was brought on by increasingly warm and humid air arriving from France.
BBC Weather said there had been more 1,000 lightning strikes across the UK overnight, although the thunderstorms are easing.
Forecasters are warning of the potential of a "second wave" of downpours later on Thursday.