The amber warning has now been issued for Sunday, July 17, Monday, July 18, and Tuesday, July 19.
The amber warning highlights likely adverse health effects for the public, which are not limited to the most vulnerable.
Temperatures could be in excess of 35 degrees celsius in the south east, and more widely around 32 degrees celsius within the warning area, with Monday and Tuesday most likely to see temperatures around this level.
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Met Office deputy chief meteorologist Dan Harris said: “Maximum temperatures have been well above average almost everywhere in the UK this week, the exception perhaps being the Western and Northern Isles of Scotland.
“Following a return to nearer average, locally rather cool temperatures over the next few days, the warm weather looks likely to steadily ramp up once again this weekend, probably peaking early next week.”
Dr Agostinho Sousa, head of extreme events and health protection at UKHSA, said: “Heat-health alerts have now been issued to the majority of the country, with temperatures set to remain consistently high throughout the duration of this week.
“Most of us can enjoy the hot weather when it arrives, but it is important to keep yourself hydrated and to find shade where possible when UV rays are strongest, between 11am and 3pm.
“If you have vulnerable family, friends and neighbours, make sure they are aware of how they can keep themselves protected from the warm weather.’’
Government advice is that 999 services should be used in emergencies only; seek advice from 111 if you need non-emergency health advice.
To find out more about keeping cool in hot weather, visit www.metoffice.gov.uk