The Met Office has issued an extreme weather warning for Sunday, as temperatures climbed to 32degC on Monday.
The rare amber alert covering much of England and Wales is used to warn people of potential health and transport issues caused by the heat.
It comes as Wales had its hottest day of the year with 28.7degC in Cardiff's Bute Park.
Northolt, west London, recorded a high of 32degC as temperatures in England soared.
Heathrow airport, in west London, recorded temperatures of 31.8C. The airport previously was the site of the UK's hottest day so far this year on 17 June when it was 32.7C.
The Met Office's extreme heat warning has only been issued twice before.
It came as a teenager was believed to have died after getting into trouble while swimming in a canal, near Wakefield in West Yorkshire.
The Met Office was advising people to stay indoors where possible and to drink plenty of fluid to cope with the heat.
Level three heat-health alerts, which are separate to the Met Office amber warning, are in place across the south, the Midlands and eastern parts of England.
The heat-health alerts, issued jointly by the UK Health Security Agency (UKHSA) and the Met Office, are expected to stay in place until next weekend.
Heatwaves are becoming more likely and more extreme because of climate change.
The highest temperature ever recorded in the UK was 38.7C on 25 July 2019 in Cambridge Botanic Garden.
Scotland and Northern Ireland had their hottest days of the year so far on Sunday.
On Monday, Aboyne in the Highlands hit highs of 27.5C, while Armagh reached 24.2C.
Sweltering temperatures are also affecting the north of England, with Manchester set to reach a high of 28C.
A heatwave is sweeping across Europe, with a plume of hot air coming up from Africa and northwards through Spain.
Temperatures are expected to hit 38C in Madrid and 47C in Seville on Monday.
France, Germany and Italy could see the heat exceed 40C over the coming weekend.
Dr Agostinho Sousa from the UK Health Security Agency (UKHSA) has urged people to stay hydrated and try to find shade when the rays were at their strongest in the afternoon.
The agency said the elderly, people with underlying health conditions and those who lived alone were particularly at risk.
The Met Office declares a heatwave when it records at least three days in a row with maximum temperatures exceeding a set temperature - which varies in different areas of the country.
The UK's four-level heat-health system highlights the potential health impacts of high temperatures.
The level three in place at present required health and social care workers to pay particular attention to high-risk groups of people such as the elderly and vulnerable.
Hampshire County Council was preparing to deploy gritters to deal with road surfaces being melted by the sun.
The machines were normally used to tackle snow but will instead be spreading light dustings of sand to help drivers.
Some weather models were predicting extreme heat for the UK next weekend.
BBC weather presenter Chris Fawkes said temperatures could rise to the high 30s due to hot weather across Spain and Portugal being drawn to the UK - boosting temperatures through the week and into next weekend.
Weather forecasting models suggest it is possible - though not likely - temperatures in the UK on the weekend could reach 40C.
But a Met Office spokeswoman said it did not believe the warmest weather would reach 40C - UK temperatures have never reached that point.
Impact of climate change
Climate scientist Ella Gilbert said heatwaves and hot spells were increasing in frequency, intensity and duration because of climate change.
The world has already warmed by about 1.1C since the industrial era began in the latter half of the 18th century, and temperatures will keep rising unless governments around the world make steep cuts to emissions.
In England, there were 2500 excess deaths in the summer of 2020 as a result of hot weather, while heat-related deaths in the UK could treble in 30 years, the British Red Cross predicts.
Follow the impact of wild winter weather across New Zealand today
-BBC