In pictures: London basks in sweltering temperatures
The mercury could climb as high as 33C over the next few days, which is hotter than top European holiday destinations such as Marbella, Mykonos and Tenerife.
The Met Office has also issued an amber extreme heat warning for parts of Wales, all of south-west England and parts of southern and central England.
Meanwhile, Public Health England extended its heat-health warning today, which warns people to take measures to stay cool and look out for vulnerable people, until Friday.
However, Grahame Madge, spokesman for the Met Office, warned of heavy rain amid the thunderstorms.
“The lightning frequency could be quite intense. We could see very large hail which could easily cause impact and obviously with any thunderstorms we could see those systems producing 30-60mm of rain within an hour or two,” he said.
Madge added: “The thunderstorms we’ve got developing are purely because of the heat so they’re not likely to affect the heat in anyway.
“They will bring moisture and relief but it’s not an indication of things changing fundamentally.”
Central England could see some of the highest temperatures over the next few days, forecasters predict.
Madge said: “Normally we say the south east but the focus of the heat is slightly shifted west this time. The heat is certainly likely to last up to the end of Thursday.
“From Friday onwards there is a strong signal for the heat that remains to be concentrated more towards the north and west whereas parts of England and Wales will start to come back to temperatures near normal,” Madge said.
The Met Office has also issued an extreme heat weather warning in Northern Ireland for between Wednesday morning and Friday night, with high overnight temperatures also expected.
Belfast could be as hot as 27C (44.6F) during the day on Thursday while temperatures are expected to be around 21C at night during the week.
PHE has advised people to stay safe during the hot weather by keeping well hydrated, avoiding excess alcohol, wearing sun cream and trying to keep out of the sun between 11am and 3pm.