East London's Whipps Cross and Newham hospitals urged patients to use other A&Es for urgent care, and ambulances are being redirected.
Torrential rain has caused severe flooding in homes, roads and stations.
The London fire brigade said it had taken about 300 flooding-related calls in the space of a few hours.
An amber thunderstorm warning is in place for much of south-east England, with 75 to 100mm (3in to 4in) of rainfall forecast in some areas.
Vehicles became stranded, and officials warned people not to travel in the hazardous conditions.