Temperatures are expected to reach 31C in central England on Sunday before record highs next week.
The Met Office forecast dry weather for Wales, the Midlands, south east and south west England on Sunday as temperatures soar to 31C in most places when a orange extreme heat warning goes into effect.
North West and North East England, as well as Scotland, meanwhile, are expected to have a cloudier day, with occasional showers or rain.
Highs of 25C are forecast for the North West of England, while the North East and most of Scotland could see highs of 23C.
Cabinet Minister Kit Malthouse has warned transport services will face “significant disruption” next week due to the heatwave, urging people not to travel.
Ministers held an emergency Cobra meeting on Saturday after meteorologists warned of record temperatures in England next week that could put lives at risk.
After chairing the meeting, Mr Malthouse told the BBC: ‘Obviously the carriers are sending people a message saying they should only travel if they really need to on Mondays and Tuesdays.
“Services are going to be significantly affected. Heat will affect the tracks, for example, so trains have to run slower. There may be fewer services. People need to be on their toes in case of disruption.
“If they don’t have to travel, it can be a time to work from home.”
Mr Malthouse said steps had been taken to ensure hospitals and ambulances that could come under pressure were prepared, while schools were given guidance to enable them to remain open.
He added in a separate statement: “It’s important that we all continue to follow public health advice to stay cool and take simple precautions like drinking plenty of water and seeking shade, and also watching friends. and vulnerable neighbours.”
Saturday’s kick started the start of the heatwave, with Heathrow Airport and Kew Gardens in west London recording the highest temperature of 29.1C.
Hot weather has led to increased demand for water in some areas, with South East Water confirming that residents of Challock and Molash in Kent have no water due to “hot weather continuous and significantly increased demand for water” putting “significant pressure on our network”.
A statement from the supplier said: “We are continuing to work on restoring your supplies and will continue to work on this overnight.
“As a precaution, we will be opening the bottled water station at Challock Village Hall tomorrow morning at 8am.
“The team will be here until 7 p.m. tomorrow night.”
Meteorologists have given an 80 per cent chance of the mercury exceeding the UK’s record high temperature of 38.7C set in Cambridge in 2019, with the current heat wave set to peak on Tuesday.
Scorching temperatures are forecast for Monday, with Peterborough expected to reach 37C and Milton Keynes, Norwich and Lincoln expected to reach 36C.
Temperatures are expected to rise by several more degrees on Tuesday – into the mid-30s for much of England and Wales.
There is a 50% chance that temperatures will reach 40C somewhere in the UK on that day, likely along the A1 corridor that runs from London to Scotland through counties such as Lincolnshire, Nottinghamshire , Yorkshire and the North East.
Following the publication of the Met Office’s first red warning for extreme heat, covering part of England from London to Manchester and York on Monday and Tuesday, its chief executive Penny Endersby said people may struggle to know what to expect when “climate change has caused such unprecedented severe weather events”.
“Here in the UK we are used to treating a hot spell as a chance to go play in the sun,” she added.
“It’s not that kind of weather.”
The orange warning initially covers all of England on Sunday and extends to southern Scotland and Wales from Monday to Tuesday.
London Mayor Sadiq Khan held a special meeting on Friday with key senior officials from agencies including the NHS, Met Police, London Fire Brigade, London Ambulance Service, Councils and Transport for London to ensure a solid plan is in place to deal with the level four heat alert.
Mr Khan urged Londoners to only make essential journeys on Monday and Tuesday and to prepare for disruption as speed restrictions will be in place on the rail and tube networks.
A high air pollution alert for London was also issued by the mayor for Monday.
Labor meanwhile slammed Prime Minister Boris Johnson after reports said he had failed to attend Cobra meetings.
Angela Rayner, Labour’s deputy leader, said: ‘Boris Johnson is again missing in action. He’s back to his old tricks of skipping important Cobra meetings.
“Where is the plan to deliver essential services and how will people be protected at work, in transport, in schools, hospitals and care homes?
“The public will have no faith in this zombie Tory government responding quickly and decisively to this national emergency as this disgraced Prime Minister prepares to party while Britain boils.”
The UK Health Safety Agency has raised its health heat warning from level three to level four – a ‘national emergency’.
Level four is reached “when a heat wave is so severe and/or prolonged that its effects extend outside the health and social care system…At this level, illness and death can occur among fit and healthy people, and not just in high-risk groups,” it said.
Meanwhile, Britons rushed to buy fans and looser clothing to help them stay cool during the heatwave.
Retailer Toolsstation said fan sales rose 641% in the past week from the previous week as traders struggled to stay cool.
The company also said sales of builder’s shorts increased by 50% and t-shirts by 35%.
Firefighters including the South Wales Fire And Rescue Service, Scottish Fire And Rescue and London Fire Brigade have issued safety warnings, urging people to act responsibly.
They warn people to dispose of barbecues, lit cigarettes and glass bottles responsibly, not to burn rubbish such as garden waste and to use local authority services instead, and that barbecues should not be used on balconies or near sheds, fences, trees, shrubs and yard waste to prevent any ignition.
They also urge people who cool off in streams to be aware of cold water shock.