The former Take That star wants to do up his £17million mansion in Holland Park, west London by installing a lift and a recording studio.
But his plans have not gone down well with neighbour Jimmy Page, who has objected to the changes in a strongly-worded letter to Kensington and Chelsea Council.
Williams, 40, bought the 46-room mansion from late film director Michael Winner in 2013.
He now wants to carry out a number of interior alterations to turn the Victorian mansion into a contemporary family home.
The plans - which also include the installation of a lift and a recording studio - have been poorly received by Page, who lives in the Grade I listed Tower House nearby.
The musician - whose band's hits included Whole Lotta Love - has owned the landmark home for more than 40 years and regards it as one of the most important properties in the borough.
In a strongly-worded letter to the council, Page has expressed a number of concerns.
He wrote: 'I have been responsible for the protection of the Tower House for over 40 years and I am always concerned when proposals are made for nearby properties which may be detrimental to the well-being of this important heritage asset.'
Page says because Williams' house is Grade II listed, the exterior should be considered 'sacrosanct'.
He says a new window planned will overlook the side of his house and his back garden, which will have a 'significant impact on the amenity' of his property.
The rockstar is also concerned that work on the underground swimming pool could cause 'vibrations and possible structural' damage to Tower House.
Page, aged 71, also objects to Williams knocking down part of his home's boundary wall to allow access to a planned garden car park.
He wrote: '[This] will be detrimental to the general amenity of the conservation area as well as destroying part of the attractive boundary wall.'
Williams' planning application states the building work will take place from early this month until October this year, with workmen accessing the site between 8am and 6pm on Mondays to Fridays and 8am and 1pm on Saturdays.
He promises no work will be carried out on Sundays or Bank Holidays and reversing vehicles will be guided in by 'suitably qualified banksman'.
Page bought Tower House in 1972. The 19th century, Grade I listed home was built by William Burgess and, in the 1960s, was saved from demolition after a campaign led by John Betjeman and Evelyn Waugh.
Williams' house also has a colourful history. The property was bought by George Winner for £2,000 in 1946.
It was the home Michael Winner grew up in. The Death Wish director took the property over in 1978, transforming it from three flats into his own personal palace.
Winner put the mansion on the market for £60 million in 2011, but he couldn't find a buyer.
The director passed away in January 2013, with Williams buying the home later that year for £17.5 million.
He submitted the plans to Kensington and Chelsea Council in December with the public consultation ending on January 2.
A decision on the plans is expected by the end of the month. Both parties declined to comment.
From: Daily Mail
This Month in