The two bands - who were preparing for shows at the festival's Chelmsford venue at the time of the incident - swapped offensive gestures after Groove Armada's Tom Findlay was prevented from going to his dressing room by the Kings' security team.
However, as cars transporting the 'Someone Like You' rockers to their headline slot drove past, Tom decided to display his discontent.
Bandmate Andy Cato explained: "As it became clear what all this presidential fuss was about, Tom gave the worldwide one fingered sign of dislike as The Cars went past.
"The last one stopped. The drummer, Nathan Followill, got out making 'Come On Then', type gestures. So Tom gestured 'Come on then,' back."
The Groove Armada star said Nathan retreated behind his security team, and demanded Groove Armada - along with other acts performing at the British festival - were removed from the backstage area.
Writing on Groove Armada's official website, Andy added: "The drummer went back behind his bodyguards, and, pointing towards Tom, Paul Weller, and the various other musicians who were pinned by the side of the road, said 'I want them removed'.
"The promoter came over, smoothed it over and apologised. Bearing in mind this was all happening backstage in the area shared by all the bands, it's hard to see what the Kings thought they were protecting themselves from.
"Was Paul Weller going to hound them for autographs? Was Florence Welch going to wrestle them to the ground? Or maybe Stereophonics were going to ask them to write "your sex is on fire" on an album sleeve?"