Residents of London flats overlooked by the Tate Modern have gone to the high court in an effort to stop “hundreds of thousands of visitors” looking into their homes from the art gallery’s viewing platform.

The owners of four flats in the Neo Bankside development on London’s Southbank say the use of the platform “unreasonably interferes with their use of their flats” and that the Tate is “committing a nuisance”.

Five claimants are seeking an injunction requiring the gallery to prevent members of the public observing their flats by cordoning off parts of the platform or erecting screening.

At a hearing in London on Friday, Mr Justice Mann was told that “the only satisfactory solution to a problem arising from visitors to the viewing platform engaging in ‘viewing’ towards and into the claimants’ home is to prevent visitors from doing so”.

But the board of trustees of the Tate Gallery, which is defending the claim, argues that “the claimants’ obvious remedy for being overlooked is to draw the blinds provided in their flats and, as necessary, to put up curtains”.

It adds that the development and expansion of the Tate Modern “will no doubt have contributed to the value of the claimants’ flats” and that they “cannot pick and choose” which aspects of local developments they do or do not like.

Tom Weekes QC, for the claimants, said the Tate was “operating a public viewing platform so as to encourage (hundreds of thousands of) visitors” to look into his clients’ homes and that its “invasion of the claimants’ privacy is relentless”.

An extension to the Tate Modern, which opened in June 2016, features an enclosed walkway around all four sides of the building which offers “360 degree views of London” and was visited by as many as 1 million people a year.

Weekes said that “because the visitors to the viewing platform are on a viewing platform, they don’t abide by the norms of behaviour that in everyday life protect the privacy of people in their home”.

He said visitors subject the flats to an unusually intense visual scrutiny, with some using binoculars and zoom lenses to look into the flats.

One claimant said in written evidence to the court: “When our blinds are open and the viewing platform is in use, we are more or less constantly watched, waved at, photographed and filmed by people on the viewing platform.”

Another said that on one occasion, he counted 84 people photographing the flats over a period of just over one-and-a-half hours and he also discovered that a photo of himself had been posted on Instagram to 1,027 followers, Weekes said.

Weekes submitted that “the use by the public of the viewing platform makes, at most, only a modest contribution to (the Tate’s) performance of its statutory objects” and that “very little of value would be lost” if visitors were excluded from the overlooking parts of the platform.

Guy Fetherstonhaugh QC, for the Tate, said “the claimants’ remedy for what they perceive to be a nuisance lies in their own hands”.

He added that the claimants complained about having to draw the blinds or put up curtains, but pointed out that “there is no right to a view”.

He said: “The claimants’ case really amounts to saying that the defendant should end the amenity of a substantial part of the viewing platform, and thereby deny the 360-degree view of London and the surrounding area to millions of people, purely to enshrine for the claimants an ability to enjoy their view entirely privately.”

Fetherstonehaugh said the claimants were seeking “to force the defendant to close a valued resource, and deny to the public the right to use the viewing platform for its intended purpose, merely to give the claimants an unencumbered right to enjoy their own view”.

He added: “It is not a case where the defendant is intentionally providing a platform for the claimants to be viewed … and its visitors do not ordinarily visit the viewing platform with the intention of looking at the claimants.”

Fetherstonehaugh said the platform “affords visitors and staff a unique, free, 360-degree view of London” which is “part of an overall experience designed to engage people with the arts” and that any interference with the claimants from it was limited.

He concluded: “The balance struck by the defendant is manifestly fair.”

On Friday afternoon, the parties and Mr Justice Mann will go on a site visit to the viewing platform and the claimants’ flats, with witness evidence expected to begin on Monday.