The UK continued to swelter in its first prolonged heatwave since 2006 as alert was on Friday raised to "level three", one below national emergency, for south-west England and the West Midlands.
The warning was first issued on Thursday, the hottest day of the year so far at 32.2 degrees Celsius, to alert healthcare services to help those in high-risk groups such as the elderly and young children.
The Met office raised Level-3 alert, which is one below a national emergency, for south-west England and the West Midlands, besides London and the south-east of England.
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 increase before the temperature cools down.
It is the UK's first prolonged heatwave since 2006, with six consecutive days of temperatures above 30 degrees C.
Professor Virginia Murray, head of extreme events at Public Health England (PHE), told BBC: "A level three watch means take action. For us, summer is wonderful... But the real concern is that we are not used to heat in this country.
"We are not aware of the risks. So PHE has a heatwave plan for England which was published for this summer.
"The most important advice is to stay cool yourself, drink plenty of cool drinks but look out for others, take care of the most vulnerable, take care of those who are very young, the elderly, those with chronic illnesses who may be particularly vulnerable to the heat and really to protect those as far as we can and to make sure we reduce the health impacts on them and the possible worrying level of increased deaths."
The heatwave is expected to continue into next week, with temperatures in the high 20s Celsius at the weekend, rising to 30 degrees C and above next week.
Police and fire chiefs reiterated warnings about escaping the heat by swimming in open water after four people died in separate incidents on Tuesday.
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 per cent more calls than normal during the heatwave.