LONDON -- Mohammed Ali Tavakoli was a familiar figure in the Iranian exile community here. Unemployed and on welfare, he could be found on most Sunday afternoons standing beneath an Iranian flag at Speaker's Corner in Hyde Park, London's traditional spot for proselyters and a gathering place for emigres.

Tavakoli's speech usually included a long denunciation of Iran's Islamic government. As he spoke, one of his sons would pass through the impromptu, open-air audience, distributing leaflets on the same theme.

Despite the energy he devoted to the task, however, Tavakoli's only regular followers appear to have been members of his extended family. According to a variety of sources, including the police, there was no reason to believe that he was involved in organized efforts to overthrow the ayatollahs in Iran, or that his influence extended much beyond his soapbox.

Yet early last month, Tavakoli, 58, and his son, Noureddin Navir, 24, were found dead in the family's public housing apartment, victims of what police said was an attack by agents of the Tehran government. Both had been shot several times by a submachine gun about 12 hours before their bodies were discovered.

The Oct. 2 killings were the third such attack against Iranian exiles here in little more than a year. In all, three people have been killed and one injured.

In each case, the choice of victim was puzzling. All were relatively minor players in the world of exile politics, nonviolent believers in a return to monarchy or establishment of a constitutional government in Iran.

But according to a variety of exile sources, it is because the attacks seem so pointless that they have succeeded in bringing a new level of terror to the Iranian community here.

"When the others see insignificant people like Tavakoli being bumped off," said one, "they say, jeez, what's going to happen to me?"

Until last year, Britain's 30,000-member Iranian community had been largely spared the violence that has affected such groups in other countries, particularly France.

From the police point of view, Libyan exiles, opposed to Col. Moammar Gadhafi, had the most to fear here. The spate of Libyan killings that swept Britain in the early 1980s ended only after pro-Gadhafi "student" groups were infiltrated and scores of Libyans were deported.

What is happening now with the Iranians "follows the same pattern," according to a senior security source. While police know that Tehran's agents have established a support network here and ways of entering and leaving the country undetected, the police have not been able to crack it. There have been no arrests in any of the three cases.

Some Iranians say the reason they escaped attack for so long was a tacit understanding between the British government and that of Ayatollah Ruhollah Khomeini. In exchange for a thriving trade relationship, stable diplomatic ties and British cooperation in aiding anti-Soviet rebels in Afghanistan, Tehran reportedly maintained a hands-off policy toward Iranians in this country.

British officials denied the existence of any such understanding. But they acknowledged that the first of the attacks, in August 1986, coincided with London's worsening relations, first with Iran's ally Syria, and more recently with Tehran itself.

Following diplomatic rows between the two governments, Britain last summer brought all but one of its envoys home from Tehran and ordered Iran's representation here to be reduced to one person. The dispute began when an Iranian diplomat was arrested for shoplifting. Shortly afterward, a British diplomat in Tehran was seized, beaten and held for 10 days by Revolutionary Guards.

Iranian exiles in Britain have always lived in the shadow of their counterparts in France, where most of the anti-Khomeini organizations have headquarters. Iranians who are politically active here are divided among a bewildering range of groups, some little more than printing-press operations with memberships that can be counted on one hand.

Pro-Khomeini factions, funded by Tehran, publish slick magazines and newspapers here with names like Crescent and Imam, in Persian, Arabic and English. Anti-Khomeini groups are divided between the left and nonleft, with the former being the best organized as well as the smallest.

Iranian communists are divided into at least three groups: pro-Moscow, Stalinist and pro-Albanian. Most active on the left is the Paris-based People's Mujaheddin. Begun as a student-based revolutionary group supportive of the ayatollahs, it now recruits Iranian students in British universities to join its fight against Tehran from military bases in Iraq while undertaking very little activity here.

According to various sources here, the vast majority of the exiles in Britain are apolitical. Many are presumed to be inactive supporters of the shah's exiled son, Reza Pahlavi II, 26, or some sort of constitutional or republican government.

"The nonleft is perhaps 95 percent of the population of any major capital outside Iran," said Mehrdad Khonsari, an exile who recently resigned his position as an aide to former Iranian prime minister Shahpour Bakhtiar after what he described as eight years of unproductive exile politicking.

Bakhtiar's Paris-headquartered group, the National Movement of the Iranian Resistance, espouses democratic rule in Iran. It is also believed to be a major recipient of funds from governments sympathetic to the anti-Khomeini cause, including the United States and Saudi Arabia.

The largely silent exile majority is viewed as a reservoir of support to be tapped by groups such as Bakhtiar's. Activists here said the exile majority is also seen as a major threat by Tehran, which fears its politicization and the message of encouragement that its mobilization could send to like-minded monarchists and democrats inside Tehran.

While some say the attacks allegedly organized by Tehran are meant to send a message to the British government, and some say the audience is the exiles, others believe that they are a sign of the ayatollahs' irritation at even the smallest exile insults and disrespect.

"It annoys them," said one security official. "It annoyed the Libyans. They take it as a personal affront."

Whatever the motivation, the targets seem to have been chosen to provide the most widespread terror at the lowest cost.

"If they kill one or two mujaheddin leaders here, who cares?" said a London-based Iranian journalist. "It's just two new martyrs." But if the target is a monarchist or a democrat, he said, "they scare them all."

The intended target of the first London attack, in August last year, was Reza Fazeli, a movie actor who left Tehran eight years ago because of restrictions that the ruling mullahs had placed on his work.

Fazeli was out of his shop on the morning that a bomb exploded in the basement. But it killed his son, Bijan, 22.

Unlike Tavakoli, Fazeli is well known among the exiles, but his fame stems from his movie career rather than politics.

"I am the Marlon Brando of Iran," he explained recently.

In London, Fazeli operates the House of Culture and Art of Iran, a video and book store whose extensive selection of Persian-language material has made it a popular meeting point for exiles as well as Iranian diplomats. Fazeli said his offerings are uncensored and include anti-Khomeini literature and films, some of them produced by Fazeli himself, as well as pro-Khomeini books and videos supplied in the past by the Iranian Embassy.

Some of the "cultural satires" Fazeli produced poked fun at the mullahs and have been purchased and copied for lucrative underground sale in Iran.

Security sources said they have established that the bomb was planted in Fazeli's shop by a member of Iran's Revolutionary Guards, whose name and present location -- outside Britain -- is known to them. They said the man entered the country, along with the explosives, on an Iran Air flight and left the same way.

After the bombing, the Iranian Embassy accused Fazeli of making the bomb himself and said it must have accidentally blown up before his son had a chance to plant it at the embassy.

Fazeli said he believes he was chosen as a target because of his visibility and the terrorizing effect an attack against him would have on the community.

"I now look under my car for a bomb every time I get in it and say bye-bye every time I turn the key," he said.

The next exile target did not look under his car, where a bomb had been attached. One morning last July, Amir Hossain Amir-Parviz, the London director of Bakhtiar's resistance movement, was driving along Kensington High Street when he made a sharp left turn that detonated the device. Amir-Parviz survived, suffering only a broken leg and minor injuries.

Police investigating the explosion went immediately to London's Heathrow Airport, where another Iran Air plane was laying over, but found nothing aboard that was related to the attack. The bomb, they said, was an "improvised device" that was probably made here from component parts carried into Britain in a variety of ways.