According to the website, the letter says: "The committee may not have been aware that Robbie Williams has been playing loud 70s rock music on outside speakers when he views Jimmy Page outside his home".
The musicians, who live in Holland Park, west London, clashed after the ex-Take That singer was granted conditional approval past year to build a basement swimming pool.
Williams was granted conditional approval for the work in December a year ago but Page fears the excavation work will damage his heritage-listed 1875 mansion.More news: Katie Boulter claims biggest win of career over Makarova
The local resident, known only as Johnny, reportedly wrote to the council to outline Robbie Williams' actions for the appeals process.
Williams is also allegedly imitating Page's former Led Zeppelin bandmate, Robert Plant.
"Plant was remembered for performing with his shirt open on stage, and obviously he cannot perform in this manner in his current condition, as it would be very embarrassing".
Still, their biffo is in the public domain because "Anonymous" formally complained to Kensington and Chelsea Council about 44-year-old Williams' rudeness, posting a letter on the council's planning portal.More news: Dillian Whyte fancies his chances of knocking out Tyson Fury
They will also decide whether to ask Williams for a bond, which could be forfeited if those conditions were breached or if any damage is done to Page's property.
The letter also stated that the loud music "upsets" Page.
On the other hand, a spokesperson for Robbie Williams called the claims "a complete fabrication and nonsense".
At the end of previous year, Williams' application was approved, with conditions meaning he needs to monitor vibration levels and ground movement.More news: Here’s Why Kanye West Actually Dropped Out Of Coachella 2019…
Page's representative, Mark Borkowski, said he planned to arrange a meeting between the musicians this month.