A yellow warning for storms has been issued by the Met Office for parts of the East Midlands, South East and East of England until the end of Tuesday July 20.
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.
Grahame Madge, spokesman for the Met Office, warned of heavy rain amid the thunderstorms.
He said: “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.”
Although the Environment Agency has issued 16 flood alerts for parts of the country, these alerts are concentrated around London and Nottingham. Peterborough has not been placed on alert.
Mr 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.”
The Met Office predicts the storms could hit Peterborough between 6pm and 8pm, with the weather reverting back to clear skies by nightfall.
Wednesday is forecast to be clear and bright, with the mercury anticipated to hit 29C in the city.
Central England could see some of the highest temperatures over the next few days, forecasters predict.
Mr 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.”
Public Health England has extended its heat-health warning until Friday. This warning advises 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.