Up to 760 people in England have died as a result of the current heatwave, figures show, and the death toll is set to rise further still.
Research by the London School of Hygiene and Tropical Medicine found that between 540 and 760 deaths could be attributed to the ongoing spell of hot weather.
Forecasters say the heatwave shows no signs of abating, meaning the number of fatalities is likely to double before the temperature cools down.
Ben Armstrong, professor in epidemiological statistics, produced the mortality figures for The Times using Met Office temperature data and comparing it to previous studies he has conducted on other British heatwaves.
The numbers cover the nine-day period from July 6 to last Sunday, which is the most recent date for which data is available.
The Met Office yesterday issued a level 3 heatwave alert, meaning social and healthcare services are advised to take specific actions that target high-risk groups.
The elderly and the young, and those with chronic health conditions, have been urged to take extra care.
Professor Virginia Murray, head of extreme events and health protection at Public Health England, said: "The risk of death and risk of illness really concerns us.
"Those with pre-existing illnesses are at much greater risk of not being able to cope with heat. It's much harder for them to cope with cooling.
"Data has shown real risk of increased deaths when temperature goes above 26C."
Vulnerable people include those with breathing difficulties, who might struggle to get enough air into their bodies to regulate their temperature, and those with heart conditions, who were more likely to suffer a heart attack in the heat, she said.
Very hot temperatures can also cause heatstroke, which can result in brain damage and death.
The country experienced the hottest day of the year so far yesterday, with the mercury hitting 32.2C (90F).
Temperatures are expected to hit 30C (86F) again today, according to weather forecasters at MeteoGroup.
The heatwave is expected to continue into next week, with temperatures in the high 20s Celsius at the weekend, rising to 30C and above next week.
Police and fire chiefs yesterday reiterated warnings about escaping the heat by swimming in open water after four people died in separate incidents on Tuesday.
A 16-year-old boy and a 41-year-old man from King's Lynn were found dead in unrelated incidents in lakes at Bawsey Pits, Norfolk.
A man believed to be a 21-year-old from Shropshire died after getting into difficulties near the confluence of the Rivers Dee and Ceiriog on the Shropshire-north Wales border, and a 40-year-old woman from Saltash died following what police called a "medical episode"while swimming in the sea at Seaton, near Torpoint in eastern Cornwall.
Hospitals have meanwhile seen a rise in admissions to A&E in recent days as large numbers turn up with sunstroke and sunburn.
London Ambulance Service said it had seen about 30% more calls than normal during the heatwave.
By yesterday, the country had seen five consecutive days of 30C-plus temperatures, making it the first prolonged heat wave since 2006.