By Wednesday even higher values of 37C (99F) are possible and there is a good chance that the UK’s June temperature record could be broken.
There will be tropical nights in some locations where overnight temperatures are expected to remain above 20C (68F).
This combination of hot days and very warm nights is likely to bring a range of impacts.
There is a risk to health, especially for elderly and vulnerable people.
The UK Health Security Agency has already issued separate amber and yellow heat health alerts across large swathes of England.
However, even in younger and healthier people there is a risk of conditions such as sunstroke and heat exhaustion.
People are being urged to take extra care when in and around open water, when at the coast or close to rivers and lakes.
Delays and disruption to travel networks and power supplies are possible.
Isolated downpours and thunderstorms could pose an additional hazard.
The heat is spreading from continental Europe where an extremely intense hot spell has developed.
Temperatures in parts of western France could climb to 43 or 44C (109-111F) over the next few days.
Paris is likely to reach 40C (104F) which would be unprecedented for June.