A number of London Underground lines were also suspended.
The affected rail routes included services into London Victoria from East Croydon, London Waterloo via Surbiton and a variety of metro routes in south-east London.
Passengers travelling with operators such as South West Trains, Southern, Gatwick Express and London Overground suffered delays and cancellations.
A Network Rail spokesman said flash floods were rising in some areas and its engineers were also dealing with the aftermath of lightning strikes at Surbiton.
He added: ” Our staff have been out all night and are still out in the rain working with pumps and repairing damage, and we are doing all that we can to keep trains running.”
The District line, DLR and London Overground were all suspended or delayed because of flooding.
Many of London’s roads were affected by localised flooding, including the North Circular, which was closed at Waltham Forest.
London Fire Brigade (LFB) appealed for people to only dial 999 “where there is a risk to life or property” after receiving twice as many weather-related emergency calls between 1.30am and 6.30am as the brigade usually handles in 24 hours.
It has dealt with flooded homes, commercial properties and roads, as well as vehicles trapped by floodwater and properties struck by lightning.
There have been no reports of serious injuries.
In just one hour, 0.8in (20.5mm) of rain fell in Bexley, south-east London – close to half the June average – with some parts expected to see multiple showers bringing a month’s worth of rain on Thursday morning.
A number of spots saw large amounts of rain overnight, with South Farnborough, Hampshire, recording almost 46mm (1.8in) between 7pm on Wednesday and 9am on Thursday.
Central London’s St James’s Park and Alice Holt Lodge, Hampshire, both received around 44mm (1.7in) overnight, while a number of other places in Surrey, Hampshire, London and Essex have had more than 30mm (1.2in).
The Environment Agency has issued seven flood warnings covering rivers in London and Essex, and more than 40 flood alerts across the South East.
Showers were expected to ease by 10am on Thursday morning before returning with similar intensity from 2pm.
The Met Office has issued an amber “be prepared” warning of rain for Buckinghamshire, Greater London, Kent, Surrey, Slough, Windsor and Maidenhead effective for later on Thursday.
A yellow warning covering the South East is in place until Friday.
Kingston upon Thames Council in south west London has moved two polling stations after they were inundated with water.
Polling stations in Devon Way in Chessington and Shiraz Mirza in New Malden have been relocated, while several others remain difficult to access because of the wet weather.
Heavy rain caused the closure of the cafe at the Royal Courts of Justice complex in central London.
Staff said water had leaked through a roof and flooded a kitchen.
It is understood cases have been disrupted at Snaresbrook Crown Court after heavy rain caused ceiling tiles to collapse inside some of the court rooms and corridors.
A source said: “All of our hearings have been very much delayed in their progress. We are dealing with it as best we can. The surrounding roads are flooded and a juror has been stuck in traffic for four hours.”