Good walls make good neighbours – but not, it seems, when they are made entirely of glass. Five residents of the multi-million-pound Neo Bankside towers, which loom behind Tate Modern like a crystalline bar chart of inflated land values, have filed a legal claim against the museum to have part of its viewing platform shut down. They claim that its 10th-floor public terrace has put their homes into a state of “near constant surveillance”.

Climb to the summit of the Tate’s new twisted brick ziggurat and you are rewarded with majestic views of London’s skyline, where St Paul’s dome now competes for attention with the portly stump of the Walkie-Talkie, the swollen shaft of One Blackfriars and a host of other novelty forms in the capital’s own drunken sculpture garden. But most visitors are to be found huddled around the other side of the terrace, gawping at a spectacle of another kind: the pristine still lives of rich people’s homes.

Like a vertical stack of Damien Hirst’s formaldehyde tanks, the apartments of Neo Bankside are piled up just metres away, their glass vitrines displaying glistening tableaux of Eames chairs, Castiglioni lamps and ornamental fruit in silver bowls – along with plenty of expensive telescopes for spying on the surrounding panorama. But it seems the residents want their crow’s nest views to work only one way.

The view of Neo Bankside from the Tate. Photograph: Alicia Canter/The Guardian

The high court claim goes on to complain of the trauma of living life in a “goldfish bowl”, arguing that the “viewing platform is unreasonably interfering with the claimants’ enjoyment of their flats, so as to be a nuisance”. It suggests that the problem could be solved “at little or no cost” to the Tate “by erecting cordons” that would prevent people from accessing the southern side of the terrace. When concerns were first raised last September, Tate boss Nick Serota suggested the residents could “put up a blind or a net curtain”. So how is their case likely to fare?

“The ‘goldfish bowl’ is the key,” says Paul Greatholder, expert in property disputes at Russell-Cooke solicitors. “The point that will be made in court is that these people voluntarily bought a goldfish bowl to live in. All that’s happened is that someone has built a viewing platform that means you can look into the bowl. There’s an inherent contradiction in people buying flats with huge windows in central London out of which they can look anywhere, but not wanting people to look inside.”

It is particularly odd that the claim is being brought by residents of a development where the towers are packed so close together that they can already see into each other’s homes. Nor should the Tate’s viewing terrace have come as a surprise. The museum’s plans were already well known when the flats went on sale, and the developers of Neo Bankside had actively supported the museum’s extension.

Commenting on the original planning application, which received permission in 2009, Neo’s owners, GC Bankside, stated that it “strongly supports the latest proposals, which will increase the attractiveness of the location as a visitor destination and will result in a number of other positive benefits for the area”.

The arrival of the £260m Switch House would clearly add to their bottom line – indeed the presence of the Tate was the very reason this luxury development was built here in the first place. “Move in next door to Warhol, Dalí and Picasso,” cooed the advertisement for the flats, published in Tate’s own magazine in 2011, and “brush shoulders with some illustrious arty types.” As long as the arty types don’t come too close, or have the temerity to look back.

It is an iniquitous phenomenon that is happening across the city and beyond, where the very things that make an area attractive – and prompt the influx of property speculators – are then cast as nuisances to be wiped out. In Wapping, where docklands warehouses have been bleached of character by luxury flats, neighbours succeeded in hounding out the post-industrial cool that had lured them there in the first place.

Before Tate Modern had even happened, curator Jules Wright had the imagination and foresight to transform Wapping’s hydraulic power station into a beguiling arts venue and restaurant, where visitors could dine among Victorian turbines and experience performances in an inky well not unlike the Tate’s tanks.

But the occasional evening merriment of visitors departing the Wapping Project was too much for some of the curtain-twitching loft-dwellers to stomach. They complained to the council and prompted the venue’s closure in 2013. As curator Wright put it: “As Wapping settles into a well behaved neighbourhood, closer in spirit to a Surrey village than an inner London borough, and the developers move in to complete the gentrification, the time has also come for us to move on.”

The .Cent and Fabris Lane Triptych Party, held at the Wapping Project in 2009. Photograph: Dave M Benett/Getty Images

Countless pubs and music venues across the country are under threat for similar reasons as the national obsession with protecting house prices threatens to turn lively urban areas into lifeless dormitory towns. In aggressively trying to safeguard the value of their assets, incoming residents are relentlessly lobotomising the cities they want to call home, ironing out the edgy “vibrancy” on which they were sold their dream of urban living. Everything from cultural venues to manufacturing sites are increasingly vulnerable to retroactive nimbyism, because in UK law there is no provision to protect something that is already there from what comes after.

“If someone knowingly moves to an existing nuisance,” says Greatholder, “it is still a nuisance.” He says the “law of nuisance” – which has developed through case law over the last two centuries – has undergone a radical shakeup in recent years since the landmark case of Coventry v Lawrence in 2014. The action was brought by a couple who moved into a house next to an existing racing track and then realised that life with a constant soundtrack of motorbikes and stock cars wasn’t to their taste.

Remarkably, the claimants were granted damages and an injunction against the racing track, which had existed since 1975. The Supreme Court upheld the ruling on appeal, dismissing the track owner’s defence that the new residents “came to the nuisance”. The court held that when someone uses their property for the same purposes as their predecessor (ie, as a dwelling), the argument that they came to an existing nuisance does not constitute a defence. The couple may have won, but during the protracted case their house burnt down.

Ministry of Sound nightclub in Elephant and Castle, south London. Photograph: Johnny Green/PA

With a new development, the nuisance case is harder to argue, but that didn’t allay the fears of the Ministry of Sound nightclub in Elephant & Castle, London, when a 41-storey tower of luxury flats was proposed on its doorstep. After prolonged negotiations, the developers agreed to incorporate high levels of noise reduction in the new tower, including sealed windows and internal “winter gardens”. Crucially, residents will sign away their rights to complain about noise through a reference in their deeds, preventing nuisance claims being brought in future.

As for the Tate, it is not only experts in nuisance law who should wait with bated breath. If the residents succeed in their curtain-phobic crusade, it will set a precedent for the future of our cities, undermining the very basis of tolerance on which civic life is built. It would mean that you could build a block of flats on an existing public square, then seek to have the space shut down at night when you decide that human activity in the square constitutes a breach of your human rights to stride around naked without blinds. It would mean that the non-dom residents of Dubai-on-Thames in Nine Elms could insist on an embargo on river traffic passing their balconies, or that the neighbours of schools could demand a ban on playtime.

It is the kind of case that shouldn’t even waste a judge’s time, yet given the nature of the parties involved, it is likely to run and run. “A great deal of money and expensive lawyers will be thrown at this,” adds Greatholder, “when actually a pair of curtains would do.”