The former Take That star has applied for planning permission to modernise his $28 million (£17.5 million) home by reducing the size of the swimming pool and adding a recording studio.
The application states that Williams wants a "contemporary standard of family living" for the house he bought in 2013, but nearby residents, including Led Zeppelin star Page, are said to be extremely concerned about the plans.
Britain's The Sun newspaper reports that Page sent a complaint to London's Kensington and Chelsea Council voicing his frustration over the renovations.
In the letter, Page is said to complain that a new window will overlook his garden and suggest the work will create an eyesore on their street.
A decision on the proposal will be released next month (Feb15).