They warn that significant impacts are likely across social and health care services due to high temperatures.
Impacts are likely for those over 65 or with health conditions but there may also be impacts to younger age groups too.
Amber alerts are in place for all regions of England, aside from the North East, which is under a Yellow alert for the same period.
The heatwave will start to develop from Tuesday and then intensify for many, peaking on Thursday or Friday.
And just as we saw during the June and July heatwaves, it will be extreme for some with temperatures into the mid-30s Celsius.
The hottest weather on Tuesday is likely to be across the Midlands, central southern England and east Wales where temperatures will rise to 28 to 30C.
By Wednesday the heat will spread more widely across England and Wales, with temperatures widely 30 to 32C.
Then by Thursday, even hotter still with the temperature exceeding 35C for some in the Midlands, eastern and south-east England.
The heat will persist on Friday for most but turning less hot across western areas - and then for all over the weekend as the heatwave eases.
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