Several drownings were reported in Britain and France as people tried to cool down.
A temperature of 35.1C was recorded in London on Tuesday, Britain's Met Office weather service said, breaking the 34.8C record set a day earlier.
The provisional readings smashed the long-standing record of 32.8C set in 1922.
London also recorded a rare "tropical night", defined as one in which the temperature does not fall below 20C.
Records also fell in France, where temperatures reached 36C on Monday and remained above 20C at night.
The national weather service, Météo-France, said a "heat dome" with heat held in place by a high-pressure weather front, was producing temperatures more than 10C above what is usual.
Unpredictable and extreme weather is becoming more frequent as the earth warms.
Experts say unprecedented and deadly weather extremes that sometimes strike at abnormal times and in unusual places are putting more people in danger.
"Heatwave events such as this have been made more likely and more severe due to climate change arising from our emissions of heat-trapping greenhouse gases," said Peter Thorne, director of the ICARUS Climate Research Centre, at Maynooth University, in Ireland.
"But, nevertheless, many of the records being set, particularly in the UK and France, are mind-bogglingly crazy," he said.
A long weekend sent people in Britain flocking to beaches, pools and shady parks, while London commuters sweltered in subway carriages without air conditioning.
The UK Health Security Agency issued an amber health alert for large parts of the country through to Thursday, warning of health risks, particularly among older people.
The UK is used to moderate temperatures and many homes, schools and businesses don't have air conditioning.
At least four teenagers drowned in UK lakes and reservoirs and a 60-year-old man died in the sea, authorities said.
French government spokesperson Maud Bregeon said there had been reports of at least seven deaths potentially related to high temperatures, including five drownings and two deaths in sports competitions.
The unseasonable heat extended to Spain, where weather service spokesperson Rubén del Campo said: "We find ourselves with temperatures we normally see in the middle of the summer now in the month of May".
Seville hit 38C over the weekend, while large parts of the Iberian Peninsula saw temperatures five- to-10 degrees higher than normal.
10°C