There are growing concerns people’s lives could be at risk as the Met Office indicated it is likely a new UK record temperature could be set early next week.
Meteorologists have said there is an 80% chance the mercury will top the UK’s record temperature of 38.7C (101.7F) set in Cambridge in 2019.
The heatwave is set to peak on Tuesday, with temperatures climbing over the weekend.
The Met Office has issued an amber warning for heat covering much of England and Wales from Sunday until Tuesday.
Find out the five-day forecast for where you live
Daytime temperatures on Saturday are predicted to be around 27C in London, 26C in Cardiff, 23C in Belfast and 21C in Edinburgh. On Sunday, it could hit 30C in the capital, 27C in Cardiff, 24C in Belfast and 23C in Edinburgh.
Temperatures are set to increase further across the nation on Tuesday and reach the mid-thirties for much of England and Wales.
There is a 50% chance of temperatures reaching 40C somewhere in the UK, with the Met Office issuing its first-ever red warning for extreme heat.
The UK Health Security Agency increased its heat health warning from level three to level four – a “national emergency“.
Level four is reached “when a heatwave is so severe and/or prolonged that its effects extend outside the health and social care system… At this level, illness and death may occur among the fit and healthy, and not just in high-risk groups,” it said.
The Met Office’s red warning for Monday and Tuesday covers an area from London up to Manchester, and up to the Vale of York.
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Met Office spokesman Grahame Madge said: “If people have vulnerable relatives or neighbours, now is the time to make sure they’re putting suitable measures in place to be able to cope with the heat because if the forecast is as we think it will be in the red warning area, then people’s lives are at risk.
“This is a very serious situation.”
A No 10 spokesman said railway speed restrictions may be needed on “some parts of the network next week to manage the hot weather and to avoid any potential damage”.
Jake Kelly, of Network Rail, warned journeys will take “significantly longer and delays are likely as speed restrictions are introduced to keep passengers and railway staff safe”.
Train operators have warned passengers to avoid anything but “absolutely necessary” travel on Monday and Tuesday.
Some schools across the south are also closing on those days.
Motorists have been advised to make their journeys out of the hottest periods of the day, particularly if they have older cars.