The Met Office says there is a 70% chance of these temperatures being reached in London, the South East and eastern England this week.
An official heatwave is also possible throughout the rest of England and Wales, but the likelihood is lower - for example, 60% in the Midlands and 40% in north-east England - where temperatures in the mid- and upper-20s are most likely.
Helen Chivers, from the Met Office, said: "Thursday looks like it will be the hottest day of this spell."
How hot will it be where you are?
In southern Scotland, 22C to 23C is expected, possibly rising to 25C later in the week. Highs of about 20C are likely in the northern isles.
In Northern Ireland, Wednesday looks set to be the hottest day, reaching 23C.
The high temperatures will be accompanied by high humidity and heavy, thundery showers, the BBC Weather Centre said, with western areas likely to see the wettest weather.
Various parts of England were hit by severe thunderstorms on Saturday night.
In Birmingham, a 17-year-old boy suffered a cardiac arrest and five others were hurt in a lightning strike.
Officials had already said this summer may be warmer than the past couple of years.
With climate change, heatwaves are likely to become more common over the next few decades and the chief medical officer has warned of an increase in deaths in times of hot weather.
The Department of Health has advised people to keep their homes as cool as possible and said remembering the needs of friends, relatives and neighbours who could be at risk was essential.
Older people, especially those on medication, can often find coping with the heat particularly difficult
"Windows should be kept shaded and closed when the temperature is hotter outside than inside.
"People with respiratory problems should stay inside during the hottest part of the day," a DoH spokesman said.
Other advice in the government's heatwave plan includes to drink cold drinks such as water or fruit juice regularly and avoid hot, caffeinated drinks like tea and coffee, as well as alcohol.
Help the Aged and Age Concern welcomed the advice.
A spokesman said: "Older people, especially those on medication, can often find coping with the heat particularly difficult."
Pets' charity The Blue Cross warned owners that animals could also suffer in hot weather.
Chief vet Caroline Reay said: "Never leave pets in a car or enclosed warm space. Just a few minutes, even with an open window, can be fatal to animals."
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