DJ films clip for Capital Breakfast
Inspired by the terrible UK weather, the pair have called their version British Summertime.
They got Will to record new lyrics during a visit to their London studio.
The 44-year-old US star talked about scantily clad women and hot weather in the original, but the new version is a more realistic description of summer in Great Britain.
‘It’s a little bit chilly and cold and wet,’ he raps.
‘What about the pool, the zoo?
‘It ain’t hot yet.’
Lisa, 41, and co-presenter Dave, 34, filmed an accompanying video while hanging out on a yacht in the rain.
The new track might be about wrapping up warm, but that didn’t stop Lisa stripping down to her bikini for the shoot.
Wearing just string swimwear and a fur coat, she snuggles up to Dave and drinks tea from a flask as they travel along the Thames.
‘For all asking,’ Tweets Dave.
‘I can confirm that those are @Lisa_Snowdon real life vocals and her actual boobs on ‘British Summertime’ #willsmithBST.’