Source: This Day In Music
The original plan was to perform a track together, live, with Bowie performing at Wembley Stadium and Jagger at John F. Kennedy Stadium, until it was realized that the satellite link-up would cause a half-second delay that would make this impossible unless either Bowie or Jagger mimed their contribution, something neither artist was willing to do.
In June 1985, Bowie was recording his contributions to the Absolute Beginners soundtrack at Abbey Road Studios, and so Jagger arranged to fly in to record the track there. A rough mix of the track was completed in just four hours, at which point the pair went straight out to London Docklands to film a video with director David Mallet. Thirteen hours after the start of recording, this also was completed. Jagger arranged for some minor musical overdubs in New York.
The video was shown twice at the Live Aid event. Soon afterward the track was issued as a single, with all profits going to the charity. "Dancing in the Street" topped the UK charts for four weeks, and reached number seven in the United States.
Bowie and Jagger would perform the song once more, at the Prince's Trust Concert on June 20, 1986.
The song has been featured since on several Bowie compilations. It was also shown in movie theaters before showings of "Ruthless People", for which Jagger had recorded the theme song. It was the first instance in which a promotional clip was used outside of MTV or broadcast television. Source: Wikipedia
Oh, you know that's A Bit Of Groovy!