The hot weather has claimed the lives of hundreds of people in just nine days, scientists said.
Researchers estimated that the heatwave has led to 650 deaths in England between July 6 and 14 as the soaring temperatures show no sign of abating.
Ben Armstrong, professor in epidemiological statistics at the London School of Hygiene & Tropical Medicine, said that the hot weather could have led to the premature deaths of between 540 and 760 people.
Health officials have advised people to stay cool, drink lots of cold fluids and keep an eye on those they know to be at risk.
Professor Virginia Murray, head of extreme events and health protection at Public Health England (PHE), told The Times: "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." She told the newspaper that people with breathing difficulties could find themselves struggling to get enough air to regulate their temperature. And those with heart difficulties are also more likely to suffer heart attacks, she said.
Dr Angie Bone, heatwave plan leader for PHE, said: "In this continued hot weather, it's important to remember that high temperatures can be dangerous, especially for people who may be vulnerable such as older people, young children and those with serious illnesses. During very hot weather, pregnant women and people who have chronic illnesses, including cardiovascular, respiratory, renal conditions, diabetes or Parkinson's disease, may experience discomfort if indoor temperatures are particularly hot and in using public transport."
Prof Armstrong created the mortality statistics for the newspaper by using temperatures supplied by the Met Office and comparing it with studies he has conducted during previous heatwaves in Britain.
The news comes as the Met Office has raised heatwave alerts in more parts of Britain. South West England and the West Midlands have been elevated from level two to level three, putting the regions on a par with the South East and London. The country experienced the hottest day of the year so far on Wednesday, with the mercury hitting 32.2C (90F).
Firefighters fought a grass fire which burnt through the equivalent of four football pitches in Mitcham, south London, following warnings that the heatwave made such blazes more likely. Three fire engines and around 15 firefighters were called out to Mitcham Common at midday on Thursday. It took them until 1pm to bring the flames spreading across four hectares of grass and gorse under control. London Fire Brigade (LFB) says it has dealt with twice as many grass fires in this summer's heatwave compared with last year. Dave Brown, LFB's head of operations, said: "A small spark from a cigarette is often all it takes to start a grass fire in these dry conditions. It really is important that smokers dispose of their cigarettes properly. Drivers also need to take care not to throw cigarettes out of car windows as they can easily burn grass verges. If you see a grass fire, don't attempt to put it out yourself as grass fires can be fast-moving and change direction without warning. Call the fire brigade and let us know where the fire is."
In Wales, doctors at the Abertawe Bro Morgannwg University Health Board reported seeing their plastic surgery trauma cases double to 53. Medics warned about the dangers of ride-on lawn mowers. Dean Boyce, consultant plastic surgeon at the Welsh Centre for Burns and Plastic Surgery at Morriston Hospital in Swansea, said: "Unfortunately we are treating a patient with a very severe foot injury, and this is not the first time this has happened. We have seen children who have lost a foot after falling off a parent's lap riding a ride-on mower. We would warn people to avoid letting anyone ride on their lap for fun because in fact this is very dangerous as the mower's safety cut out will not engage if they fall off." Other cases have involved overheated dogs biting their owners; people doing a spot of DIY having their fingers chopped off by power tools, and an increased number of cases involving patients with gout and kidney stones after they have tried to cool down by drinking beer. Emergency medicine consultant Mike McCabe said: "If you are thirsty, drink water. If you are already dehydrated and drink a cold beer, you are likely to end up even more dehydrated and you may get drunker as well. There is also a risk of dehydration and the onset of acute gout and kidney stones in those prone to these conditions. Alcohol has a stronger effect if you are dehydrated."