What happens in Vegas, it turns out, really does stay in Vegas.

The American company behind the Sphere, the gargantuan orb that shimmers, twinkles and glows just off the Las Vegas Strip, has formally withdrawn its proposal to build a sister Sphere in London.

Declaring that the plan had become a hostage to political rivalries, Madison Square Garden Entertainment said this week it would take the “groundbreaking technology” to other, more “forward-thinking cities.”

The decision was not a major surprise: Last November, London’s Labour Party mayor, Sadiq Khan, blocked the Sphere, which would have been built on a 4.7-acre site next to the Queen Elizabeth Olympic Park in Stratford, in East London.

The exterior of the building, wrapped in 54,000 square meters of LED lighting, would have been a glaring source of light pollution for nearby residents, Mr. Khan concluded.

But some argued that the rancorous demise of the Sphere attested to the complexities of building large projects in Britain. The Conservative national government, citing budget constraints, recently scaled back a high-speed rail line between London and Manchester that was a cornerstone of its plan to spread economic prosperity to the north.

Planting a Vegas knockoff on the site of a former parking lot next to a commuter train station did not generate the kind of aesthetic debates that have dogged other major projects in London. But it agitated neighbors who did not relish the prospect of opening their curtains to what is, for all intents and purposes, a vast advertising billboard, with enough wattage to outshine the glitter palaces of the Strip.

An expert review commissioned by the Greater London Authority, written by the engineering group WSP, found the project could lead to “significant harm” to residents’ health because of the impact of the Sphere’s artificial light; stroboscopic and flicker effects; and the visible and changing light intrusion. “These adverse impacts can cause annoyance, anxiety, and other adverse effects,” the report’s authors wrote.

While the Sphere would have been built with private money, the project had to go through a multilayered approval process in which both the Labour mayor and the Conservative government had a say. Even after Mr. Khan nixed the project, Michael Gove, the minister in charge of housing, put a hold on the ruling, raising the possibility that the government could overturn the mayor.

MSG Entertainment’s chief executive, James L. Dolan, was not interested in going another round. In a letter on Monday to the planning inspectorate, the global head of government affairs, Richard E. Constable, said the company, which spent an estimated $2.3 billion on the original Sphere, would take its concept elsewhere.

“After spending millions of pounds acquiring our site in Stratford and collaboratively engaging in a five-year planning process with numerous governmental bodies, including the local planning authority who approved our plans following careful review,” Mr. Constable wrote, “we cannot continue to participate in a process that is merely a political football between rival parties.”

It is a deflating end to a project that began with considerable fanfare in 2018. Even Mr. Khan initially welcomed the announcement of the Sphere, saying that it would cement London’s reputation as a mecca for live music.

With a capacity of 21,500 seats and the world’s largest and highest resolution LED screen, the Sphere could have made London a European counterpart to Las Vegas for highly lucrative concert residencies, much like the one that the Irish band U2 is currently playing in the original Sphere.

London is no stranger to eye-popping edifices: The London Eye, the giant observation wheel on the south bank of the Thames, and the Millennium Dome, now the O2 Center, opened within weeks of each other at the turn of this century. Though they drew cavils at the time, both became landmarks on the city skyline.

“All these large cities have huge, old industrial hinterlands, where it is acceptable to put things that you would never put in your historic city centers,” said Tony Travers, a professor of politics and authority on city planning at the London School of Economics. “Paris is quite capable of building Disneyland.”

What made the site purchased by MSG Entertainment particularly attractive, Professor Travers said, is that it is not far from central London and is adjacent to a major rail link. But those qualities would also have made the Sphere more intrusive to its neighbors than if it had been built on a larger site farther from town.

Residents complained they would have to install blackout blinds to keep out the glare, while competitors warned it would cause traffic chaos. In London’s cumbersome planning process, opponents have multiple chances to block projects, since they must be approved by the borough, a planning inspector and the mayor — and all of those permissions can be reversed by a cabinet minister.

“What message does that send?” Professor Travers asked. “If you’re an investor sitting in an overseas capital, what would you make of the London planning process? It’s not a very effective ‘Britain is open for business’ sign.”

While some opponents — including the company that operates the nearby O2 Center as a concert venue — questioned whether the Sphere would be out of place in a city like London, others dismissed that concern as overly precious.

Rowan Moore, the architecture critic of The Observer, a London newspaper, noted that designers have long draped buildings in dazzling light shows. In the 18th century, he wrote in a column in October, they used whale oil lamps to jazz up the Bank of England.

“It’s only the effect of time, and the disappearance of paint and decorations, that make us think of the past as mostly gray and brown,” Mr. Moore wrote.

“In which case we might embrace the Sphere,” he wrote, though he added that a London version might have “unacceptable impacts” on its neighbors.

Residents who had campaigned for years against the Sphere expressed their delight. “The dreadful MSG Sphere is dead for good!” Nate Higgins, a Green Party councilor for the area where the Sphere would have been built, said in a post on social media. “Nobody wants blackout blinds imposed on them just for the sake of advertising screens the size of Big Ben and the London Eye.”