The air chillers struggled against the thick air of an Indian summer night as members of Delhi’s fabled Gymkhana Club sipped lime sodas and ate paneer on the lawn, wondering if it might be one of the last times they could gather there.

A few hundred yards away, just over a heavily fortified wall, lives the reason for their melancholy: Prime Minister Narendra Modi, whose government served the club last week with an order to explain why it shouldn’t be evicted.

Founded more than 100 years ago as a whites-only social club for British colonial administrators and their wives, the Gymkhana is now a refuge for Delhi’s homegrown elite. But with its imperial past, the Gymkhana is facing extinction under Mr. Modi’s campaign to purge India of what he calls a residual “slave mentality.”

The central government owns the land in the heart of the Indian capital where the Gymkhana sits — 27 lush acres with two swimming pools, a library and tennis facilities that have been a stop on the pro circuit, with 26 grass and seven clay courts. Government lawyers said in their legal filing that the club’s lease would be terminated because the land is “critically required for strengthening and securing defense infrastructure,” among other reasons serving the public interest.

But members of the club — mostly current or retired civil servants, foreign service officers, military brass and others who make up the capital’s professional class — say Mr. Modi’s government is manufacturing a land dispute to send them a message: The days when Delhi’s old elite ran India are over.

“The word ‘elite’ is being bandied about,” said Abhishek Tankha, 42, a businessman who frequents the club for its squash courts and social scene. When he hears Mr. Modi and his followers use it to describe people like him, Mr. Tankha said he understands the cultural subtext: “It’s a specific type of westernized Indian who never bought Modi’s rhetoric, who Modi thinks never accepted him.”

A former member of the prime minister’s Bharatiya Janata Party, Mr. Tankha said he believes the membership of the Gymkhana is being shamed and scorned. But, he asked, “Why shouldn’t we be proud of our own clubs?”

The stereotypical Gymkhana member, who sometimes had to wait more than 20 years before being offered a spot, is the kind of person who has lost the most clout in the “New India” Mr. Modi says is rising under his watch — a country where the secular, democratic principles of its founders are giving way to his vision of a Hindu-first nation.

The escalating battles over institutions like the Gymkhana are raising complex questions about identity and heritage in this vast country of 1.4 billion people, where a hybrid culture has evolved since Indians won independence in 1947. Indians have adapted many British imports to suit their tastes, from their love of cricket to their tea culture.

Yet the racial subjugation that was so fundamental to British rule left scars that may not ever heal. Mr. Modi, who is now serving his third term as prime minister, has displayed a powerful instinct for connecting past injustices to the present, speaking to the anxiety among the Indian masses for whom membership of a private club is unthinkable.

Across Delhi, examples of Mr. Modi’s colonial erasure are everywhere — in gleaming new government buildings that have replaced turn-of-the-century sandstone palaces, and on street signs with Hindi and Sanskrit names where Englishmen’s used to be.

Within the last few weeks, the Modi government has stepped up its efforts to seize two other colonial era landmarks in Delhi, including the Jaipur Polo Ground, where King Charles III, then Prince of Wales, once played.

“In the journey of a developed India, it is vital to move forward free from the colonial mind-set,” Mr. Modi said in a speech celebrating the opening of a government complex in Delhi that includes a new office for himself, which he christened with a Sanskrit name, Seva Teerth. The buildings being replaced, however historic they may be, “were built as symbols of the British Empire, intended to keep India chained in slavery for centuries,” Mr. Modi said.

Plans call for converting the two most iconic buildings — twin fortresses known as the Secretariat — into a national museum.

By taking on the Gymkhana, Mr. Modi is endeavoring to conquer one of the most potent symbols of the British Raj. Clubs just like it all over British India — with white neoclassical clubhouses, large verandas and expansive lawns — were social hubs for the ruling elite. George Orwell centered much of the action in his novel “Burmese Days” at one such club, the Kyauktada, describing it as “the real seat of the British power.”

Only in the waning days of the empire did the clubs begin admitting Indians.

“Gymkhana Club is not merely a club,” said Rakesh Sinha, a former B.J.P. representative in the upper house of Parliament who has championed Mr. Modi’s effort. “It was a feudal arrangement,” he added, insisting that such institutions “have no space in the capital, where people are still struggling to find basic housing.”

Shutting down the club, Mr. Sinha said, “is in the interest of the common people.”

But critics of Mr. Modi’s approach to reckoning with India’s past say he is slapping a “colonial” label on institutions that have been thoroughly Indian for decades.

“Every civilization advances like this,” said Swapna Liddle, a historian and conservationist in Delhi. “You take what is there in your past, you reshape it, redesign it, repurpose it and continue to use it.”

India, Ms. Liddle added, has decolonized many institutions over the years, including the Gymkhana. “It started out as a racist, racially segregated club,” she said. “It was very much a British colonial product. It was then adapted to Indian conditions.”

Efforts to de-Anglicize long preceded Mr. Modi’s rise and have often had broad support. It was under the government of the rival political party, Congress, that parts of the Delhi cityscape were renamed in the years after independence. Queensway, one of the main north-south thoroughfares, became Janpath, or People’s Way in Hindi.

India has also renamed some of its best-known cities, changes which were not universally popular. Bombay became Mumbai in 1995; Calcutta became Kolkata in 2001. More recently, the legislature in the southern state of Kerala approved changing its name to Keralam to reflect the local tongue.

Indianization has taken many forms, even changing what people wear. At graduation ceremonies, mortar boards and gowns that were once standard issue have been replaced by loosefitting tunics called kurtas.

Mr. Modi is the first Indian prime minister born after independence, and Indianization was a priority for him well before he assumed power in 2014. Under his watch, Indianization has broadened to target relics of India’s historical periods of Muslim rule.

In February, Mr. Modi inaugurated perhaps his most ambitious architectural testament to decolonization yet: a new office complex to replace the Secretariat buildings that housed much of the government work force — and before 1947, the colonial administration.

He framed the moment in civilizational terms, as he often does when talking about India’s relationship with the West. People would look back and say this was “when India redefined its destiny,” he declared.

At the Gymkhana, members thought they might have gotten a reprieve. Mr. Modi’s administration had tussled with the club in the past over allegations of financial mismanagement, but little happened.

Then came an order in May to vacate by June 5, followed by the notice last week for the club to appear before the government land office to plead its case. A hearing has been scheduled for the end of the month.

Urmila Gupta, 82, became a member in 1984 when the club first gave voting privileges to women. She sounded forlorn at the thought of losing a place that became her second home in retirement. “People used to say the club has the best grass courts east of the Suez,” she said. “It has a legacy. And it has the right to exist.”

Amman Singh, 29, a furniture designer, grew up playing tennis at the club on a membership passed down from his late grandfather, a former army general.

Mr. Singh said the prime minister’s grievance with the club made little sense. “Why is this land, the land the Gymkhana club is on, so important to him?”

Like many younger people who use the club, Mr. Singh is not technically a member. He said when he applied several years ago, the wait was an estimated 28 years. There is little question, he acknowledged, that the club remains off limits for most people who live in Delhi.

“The club is, of course, exclusive,” he said, before quickly clarifying. “It is not elite.”