Rail passengers are being advised not to travel today, or to allow extra time for their journeys, because of speed restrictions being imposed due to the heatwave.
Southeastern, Southern and Thameslink are all running a "significantly reduced service".
Public Health England has maintained a level three heat health watch for eastern areas of England, where temperatures topped 30C on Wednesday.
The current record of 38.5C was set in Faversham in Kent in August 2003.
Councils have called on the public to check on family and friends, warning that the elderly and those with heart and respiratory problems are most at risk from the hot weather.