The musician and environmental activist said he will donate £1,000 to charity if water boss Lawrence Gosden accepts his dare.
The TV presenter vented his frustration on Twitter when he was told to delay his harvest amid the heatwave.
The Amber grading warns of adverse health effects for the general public, not just the most vulnerable to extreme heat.
After the UK's temperature record was smashed last week, climate change was at the forefront of weather reporting.
Heatwave sweeping southern Europe heads to the north of the continent, with authorities declaring national emergencies.
Conservative MP Sir John Hayes said the UK was 'cowardly' for being frightened of the life-threatening heat coming on Monday and Tuesday.
Modelling from researchers shows the UK will hit 40C more and more often if carbon emissions continue and global warming is not curbed.
Health authorities have warned people to practise caution in the hot weather, staying hydrated, applying sunscreen and not leaving children or pets in cars.
The comedian slept on her kitchen floor with the back door open due tot he heat - and was disturbed by a foxy prowler in the night.
Charity pleads for animal-lovers to protect their pets as the UK faces the hottest day of the year so far.