Deaths were up in all seven weeks from June 2 to July 20, which saw temperatures reach as high as 95F (35C).
A total of 955 people more than the average have died in England and Wales since the summer began, according to the Office for National Statistics (ONS).
Experts warned of the worst excess summer death toll since 2003, when 2,139 people died amid a record 101.3F (38.5C) heatwave.
Many of those who have died this summer are pensioners, who are less able to deal with extreme weather conditions.
Malcolm Booth, head of the National Federation of Occupational Pensioners, said the figures were “terrible” and a “tragedy for families affected”.
He told the Daily Mirror: “It’s the extreme heat which is killing people.
“This summer risks excess deaths approaching the very high figures seen in 2003.”
Public Health England (PHE) said there was “strong evidence” that excess summer deaths are “the result of heat-related conditions”.
Last month, MPs warned that the number of people dying because of heatwaves could treble by 2050.
An alarming report by the cross-party Environmental Audit Committee said Britain was “woefully unprepared” for killer heatwaves.
It found that there were almost 400 heat-related deaths on the hottest day of 2016 alone.
Mary Creagh MP, the committee’s chair, said: “Heatwave warnings are welcomed as barbecue alerts, but they threaten health, wellbeing and productivity.
“The Met Office has projected that UK summer temperatures could regularly reach 101.3F (38.5C) by the 2040s.
“The Government must stop playing pass the parcel with local councils and the NHS and develop a strategy to protect our ageing population from this increasing risk.
“There will be 7,000 heat-related deaths every year in the UK by 2050 if the Government does not take action.”
In late June the Met Office and PHE issued a Level 2 heatwave alert, putting hospitals on alert for an increase in admissions.
PHE’s Dr Owen Landeg warned Britons that the “summer heat can bring real health risks” especially for people with “underlying health conditions”.
He said: “That’s why we’re urging everyone to keep an eye on those you know who may be at risk this summer.
“If you’re able, ask if your friends, family or neighbours need any support.
“And if you’re going outside for a prolonged period, remember UV is high at this time of year.
“Think how the sun affects you and what you’d do to make sure you don’t get burned.”