The musicians, who live in Holland Park, west London, clashed after the ex-Take That singer was granted conditional approval previous year to build a basement swimming pool.
The latest development in their feud, which has been going for five years, ever since Williams expressed his intention to build a basement gym and pool in his home in west London, is that Williams is "playing loud '70s rock music" to "upset" Page, The Telegraph reports.
The 74-year-old Mr Page was anxious the excavation could damage his 1875 Grade I-listed mansion in west London where he has lived for more than 40 years.
The feud between the two started over construction at Williams' home in Holland Park.
A letter sent by a complainant only known as "Johnny" to the Royal Borough of Kensington and Chelsea, says Williams has been playing Page's "rock arch rival bands Black Sabbath, Pink Floyd, and Deep Purple" to annoy the guitarist.
The former Take That singer, 44, is said to have dressed up as Page's bandmate Robert Plant whenever he spotted the 75-year-old musician in his garden.
The BBC also reports work can not begin on Williams's home until councillors receive reassurance vibration levels and ground movement issues will be monitored.
New source said that Robbie Williams has mocked Led Zeppelin guitarist Jimmy Page by dressing up like Robert Plant. They will also decide whether to ask Williams for a bond, which could be forfeited if those conditions were breached or Page's property was damaged.
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".