In Granada, Spain, temperatures topped 46.6C (115.5F), with weather warnings issued for 41 of the country's 50 provinces.
Temperatures could edge a degree higher on Tuesday, potentially peaking at about 34C in Essex or Norfolk, the Met Office said.
Temperatures in many parts of Spain and Portugal will remain above 40 Celsius at least until Sunday, and could rise a further 2 or 3 degrees. The elderly and those with pre-existing conditions, such as asthma and heart failure, are likely to face declining health due to exacerbation of their conditions due to weather. They were a 48-year-old man working on road works and a 78-year-old man who was working on his allotment, Cadena Ser said.
Three men died last week in Spain as a result of soaring temperatures, two in the southeastern region of Murcia and one in Barcelona, emergency services said.
Spain lowered its warnings for heat from "red" to "orange" for large parts of the south, but highs there were still predicted to reach 104 to 107. And it's certainly easier to tolerate if buildings are created to cope with high temperatures - with Mediterranean-style shutters and deep balconies and bright reflective walls.
In the capital, the streets, which are normally bustling with tourists at this time of year, were left nearly deserted as a result.
British holidaymakers overseas are being warned to avoid spending time in the sun during the hottest part of the day and to keep hydrated.
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The World Meteorological Organization says continental Europe's heat record is 48 C (118.4 F), set in Greece in 1977.
The Scandinavian country has over the past weeks had dozens of wildfires, mostly in central, western and northern Sweden, and foreign firefighters helped their Swedish colleagues.
The Portuguese Institute of Sea and Atmosphere has announced today the extension until Sunday of the red alert for high temperatures in 11 out of the 18 districts of the country.
This summer is now officially hotter than drought-ridden 1976. "The forecast is that the south peak will be lower than the north peak from the beginning of August".
A significant amount of Portugal has been placed on the highest risk level for wildfires by the Portuguese Met Office, whilst only a small amount of the north-west is considered low risk.
Britain has also had a prolonged spell of hot weather with little rain, leaving vegetation in much of the country parched.
Fresher, cooler temperatures are expected from the middle of this week, lasting throughout the weekend.