Twelve Indian families, granted a reprieve by South Africa's government a month ago to stay in the downtown area of Johannesburg officially reserved for whites, are now being evicted by their landlords, the Johannesburg Stock Exchange.

The exchange wants to knock down their apartment building for a parking lot and has served notice on the 50 Indians to be out by Thursday night.

The confrontation is likely to cause a major outcry because the stock exchange epitomizes the English-speaking business community, which likes to distance itself from the harsher aspects of the government's racial policies.

If the tenants, who are descendants of immigrants from India, refuse to leave--and they say they have nowhere to go--City Hall has been instructed to cut off their water, lights and sewer services on Monday.

Leading businessmen have been critical of the government's slowness to modify its policy of apartheid, or strict racial segregation, and are anxious to project a more liberal image abroad. The government often accuses businessmen of privately approving of apartheid while publicly trying to dissociate themselves from it. These accusations are now likely to be intensified.

Action against Indians and Coloreds (mixed race) who have drifted into the central areas of South African cities has become a particularly contentious issue recently.

Under the Group Areas Act, one of the cornerstones of the apartheid system, each race is assigned its own area--whites getting the favored areas, including the downtown sections.

The system has resulted in a severe shortage of housing for the blacks. As the affluent whites have moved into the suburbs, leaving more central city apartment buildings empty, landlords have been happy to turn a blind eye to the law and accommodate desperate Coloreds and Indians.

Last year the government began to crack down on the infiltrators, prosecuting and evicting them. This led to the birth of South Africa's newest civil-rights movement, the Action Committee to Stop Evictions (Actstop). Lawyers donate their services free to fight the cases in court.

Under South African law, lawyers can only plead a defense of "necessity," arguing that the tenants should be acquitted because they have no option, given the shortage of housing.

Actstop has had little success in court, but the cases have publicized the plight of the tenants and there have been signs lately that this has sensitized the government. Several prosecutions have been withdrawn, and some buildings have been given reprieve notices.

This is what happened in the case of Arenel House, across from the Stock Exchange skyscraper.

Bibi Mohammed, who lives in Arenel House, was prosecuted Oct. 30 for living in a white area. Actstop took up the case. There was extensive publicity as Mohammed, 56, the mother of nine, told of her desperate search for accommodations.

She and her husband Ibrahim had searched in vain throughout a radius of 50 miles, she told the court.

Mohammed was found guilty, given a suspended fine of $50 on condition she did not break the law again and ordered to leave Arenel House by the end of December.

But a few weeks later the Department of Community Development, which administers the Group Areas Act, relented and gave Mohammed a permit to stay. It withdrew the charges against the other tenants and gave them permits, too.

"For Mrs. Mohammed the agony is over," reported the Johannesburg Star on its front page Dec. 10.

But it was not. She has received her notice from the Stock Exchange to be out by the end of the month.

The Stock Exchange committee's secretary, Robert Newton, said today he regarded the issue as "irrelevant."

The acting president, Paul Fergusson, said: "I am sure there is concern, but it is not in our power to find alternative accommodation for them. "We did not think we had any choice because we have a great shortage of parking."

"It will undermine everything we have gained," said Acstop's leading law adviser, John Dugard, of the University of Witwatersrand Law School. "Now the government will be able to say that if the so-called enlightened business community can do this, surely they are justified in acting, too."