The Met Office have issued a Yellow Warning for Rain (Low Likelihood of Medium Impacts) for the southern fringes of the capital, valid until 7pm this evening.
You can view further details of this warning Met Office website<http://www.metoffice.gov.uk/public/weather/warnings/#?tab=map>.
Some places in London have already seen rainfall totals of 30-40mm over the past 24 hours. Heavy rain is continuing through this morning and could produce another 15-25 mm of rain within a few hours, clearing eastwards by early afternoon.
As temperatures rise through today, some heavy showers and isolated thunderstorms are expected to develop, these most likely on the southern fringes of London (ie Sutton, Croydon and Bromley) this afternoon. Localised slow moving torrential downpours are possible with a risk of 20-40 mm of rain falling within 2 to 3 hours which could give rise to some localised surface water flooding and standing water/spray on roads.
Once the heavy rain has died out this evening we are expecting a dry evening and night. Much of Wednesday is likely to remain dry, but cloud will increase through the day to bring more rain by late evening and overnight into Thursday.