The Met Office has issued a red extreme heat warning in England, with amber warnings in Scotland and Wales.
The UK could have its hottest day on record on Monday, with temperatures forecast to hit up to 41C.
The Met Office has issued a red warning for heat across large parts of England, stretching from York and Manchester to London and the south-east.
The current highest temperature in the UK is 38.7C, in Cambridge in 2019.
High temperatures are also forecast in the rest of the UK – with amber warnings in the rest of England, all of Wales, and parts of Scotland.
London is set to be one of the hottest places in the world on Monday, with temperatures soaring above the Western Sahara and the Caribbean.
The capital is forecast to be hotter than Dakhla in Western Sahara (24C), Nassau in the Bahamas (32C), Kingston in Jamaica (33C), Malaga in Spain (28C) and Athens in Greece (35C).
The hot weather will continue on Tuesday – with overnight temperatures warned to be in the mid twenties – before cooling on Wednesday.
It is the first time the Met Office has issued a red warning since the system was introduced last year.
It means “widespread impacts on people and infrastructure” are expected, with “substantial changes in working practices and daily routines” required.
Some schools plan to close early – or not open at all – although the government has issued guidance designed to keep them open.
Network Rail said people should travel only “if absolutely necessary” on Monday and Tuesday, with some cancellations already announced, and speed restrictions in place across the network.
LNER will not run services between London and Leeds and York for much of Tuesday.
Alongside the Met Office’s red and amber warnings, the UK Health Security Agency has issued a level four warning for England, which the government is treating as a “national emergency”.
After an emergency Cobra meeting for ministers on Saturday, Health Secretary Steve Barclay said ambulance capacity would increase, alongside more call handlers.
Sunday was the hottest day of the year so far with temperatures reaching 33C in Flintshire, 32C in Cheshire, 27.7C in Armagh in Northern Ireland, and 26.4C at Auchincruive in Ayrshire.
Beaches across the country were packed, and people have been warned to take care if they cool off in water.
More on the heatwave
Water companies in southern and eastern England have warned increased demand is leading to low pressure – and even interrupted supply – for some households.
Experts have urged people to drink water, keep their curtains closed where possible, and to check on friends and relatives.
“In this country we’re used to treating a hot spell as a chance to go and play in in the sun,” said Prof Penny Endersby, Met Office chief executive. “This is not that sort of weather.”
Heatwaves have become more frequent, more intense, and last longer because of human-induced climate change.
The world has already warmed by about 1.1C since the industrial era began and temperatures will keep rising unless governments around the world make steep cuts to emissions.