It is the first time the Met Office has issued a Level 3 heatwave alert since June 2006.
It occurs when temperatures reach a certain threshold - which vary by region - and are sustained in one or more regions over two nights and the intervening day, with a forecast of higher temperatures to come.
The Met Office said a key factor in raising the alert had been night-time temperatures, with some areas not falling below 18C.
The highest heatwave level - Level 4 - is classed as "red emergency".
It is reached when heat is so severe that illness and death may occur among the fit and healthy, and not just in high-risk groups.
Met Office spokeswoman Sarah Holland said: "We are expecting temperatures in London and the South East to reach 31-32C today and on Thursday they might reach 33C.
"After that we are expecting temperatures to come down and by the weekend it should be a lot cooler."
On Tuesday, the government's health advice line NHS Direct took a total of 318 calls from members of the public complaining about sunburn, heat-exhaustion, breathing difficulties and other heat-related ailments.
The Department of Health (DoH) said those at most risk from heatstroke included the very young and the very old, and people with heart and respiratory problems.
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