The heatwave has been responsible for as many as 760 deaths, according to official calculations, as the UK enters the sixth day of plus-30C temperatures.
The temperature on Thursday hit 31.0C, following Wednesday’s year-high of 31.9C at Heathrow, marking the longest heatwave for seven years.
Research for the Times by the London School of Hygiene and Tropical medicine has estimated the death toll for the first nine days of the heatwave at between 540 and 760 people in England alone.
With temperatures set to remain high until at least the end of next week, the number of heat-related deaths is likely to double, experts said.
The Met Office issued a level-three heatwave alert on Wednesday, warning social and healthcare workers to focus on the very young, the very old and those with chronic diseases.
People with breathing difficulties could find themselves struggling to get enough air into their bodies to regulate their temperature while those with heart difficulties are more likely to suffer a heart attack.
Meanwhile, millions of households have been urged to ration water as soaring water use in London and the Home Counties puts huge pressure on the system.
Four of Britain's biggest water companies – Severn Trent, Affinity, South East and Yorkshire – told customers to cut back and use water wisely.
Affinity, a water company that supplies three and a half million homes across north London and the Home Counties, issued an alert admitting “water supply problems”. It said demand had leapt by as much as 27 per cent since the heatwave began.
“With the recent hot weather, Affinity Water has experienced a large increase in demand for water,” it said. “This has resulted in some of our customers experiencing low or reduced pressure. We have increased the production and storage of water to meet the extra demand.”
Severn Trent said that its reservoirs were not refilling as much as “we would like” overnight and urged its customers across the Midlands to turn off sprinklers when they went to bed.