The alert is in force from 2pm to 9pm on Saturday and covers cities including Manchester, Cardiff and London.
The Met Office warning says there is a “small chance” that homes and businesses could be flooded as a result of heavy rain.
Spray and excess water on the roads could also lead to car journies being delayed, it added. There is also a small chance of power cuts and cancellations to rail services.
Authorities have already issued a warning for heat this weekend with temperatures of up to 30C forecast to scorch large parts of the country.
The scorching heat prompted the Met Office and UK Health Security Agency to issue their first heat warning of the year.
It covers six regions in England, London, the East Midlands, West Midlands, East of England, South East and South West, and is in place from 9am on Friday until Monday morning.
Dr Agostinho Sousa from the UKHSA said: “In the coming days we are likely to experience our first sustained period of hot weather of the year so far, so it’s important that everyone ensures they keep hydrated and cool while enjoying the sun.
“Forecasted temperatures this week will primarily impact those over the age of 65 or those with pre-existing health conditions such as respiratory and cardiovascular diseases.
“If you have friends, family or neighbours who you know are more vulnerable to the effects of hot weather, it is important you check in on them and ensure they are aware of the forecasts and are following the necessary advice.”
It will be dry for many on Thursday evening with late spells of sunshine and some patchy cloud cover.
Conditions will remain dry overnight with clear intervals however large areas of cloud cover will build and there is a threat of a few isolated showers spreading into South West England by dawn. It will be breezy across southern England.
Friday will start dry with early clouds gradually clearing northeastwards.
It will then be mainly dry with lengthy spells of sunshine however cloud cover will build into the south-west bringing a chance of showers across south-west England and south Wales.