A tax-exempt foundation that financed two aides to Sen. Jesse A. Helms (R-N.C.) on a trip last week to London, where they caused a diplomatic flap, is only one of four set up and run by aides to Helms.

An examination of Senate records and interviews with Helms and members of his staff Thursday show that aides John E. Carbaugh Jr. and James P. Lucier hold office in the foundations, which are characterized by Carbaugh as an "innovative" strategy to "offset the liberal think tanks." Other Helms aides hold office in the foundations as well.

Carbaugh and Lucier have been accused of interfering with the Zimbabwe-Rhodesia settlement talks in London last weekend by offering encouragement to Ian D. Smith, leader of the war-torn African country's white minority.

The two aides' weekend trip to London was paid for by the Institute of American Relations, a private right-wing foundation whose founders and only officers are Carbaugh, Lucier and Dr. Victor A. Fediay, a Russian emigre who is, like Carbaugh and Lucier, a former aide to Sen Strom Thurmond (R-S.C.)

Financial disclosure statements for 1977 and 1978 filed by Carbaugh and Lucier, along with inerviews Thursday, show that, with Helms' blessing, the two also are officers either together or individually of:

The Institute on Money and Inflation. Carbaugh, Lucier and Howard S. Segermark, Helms' adviser on economics, are the only officers, according to Carbaugh.

American Familty Institute. Carbaugh and Helms aide Carl Anderson are officers with Dr. William Gribbin, whom Carbaugh did not identify.

Centre for a Free Society. Carbaugh said that he is a board member along with Dr. Fred Ikle, former director of the Arms Control and Disarmament Agency, and other conservatives.

Carbaugh said the two most active foundations -- the Institute of American Relations and the Centre for a Free Society -- took in almost $700,000 in 1978 and the first part of 1979.

He said the American Family Institute, incorporated in the District of Columbia in October, 1978, had raised "to my recollection $5,000 this year."

Carbaugh said he could not provide figures for the Institute on Money and Inflation because Helms' aide Segermark "runs that operation." Segermark was reluctant to answer a reporter's questions in a brief telephone interview yesterday morning and did not return calls yesterday afternoon.

Peter S. Ridley, District recorder of deeds, said the Institute on Money and Inflation's corporate charter was revoked in September 1978 for failure to file annual reports in 1977 and 1978.

A District Code provides that any person "who shall exercise or attempt to exercise any powers under articles of incorporation" that have been revoked "shall be deemed guilty of a misdemeanor and shall be punished by a fine not exceeding $500 or by imprisonment not exceeding one year, or both."

Segermark said in an interview earlier this week that he had traveled to Seattle at the expense of the Institute on Money and Inflation last December and to Los Angeles this year, but Ridley said he could not say whether Segermark's activities violated the District's law on revoked corporate charters.

Carbaugh said the Institute of American Relations raised about $100,000 in 1977 and $60,000 in 1976. He said the institute and the other foundations raised their money "basically by direct mail, or else people that the advisory board members know contribute."

He said Bruce Eberle & Associates handled the Institute of American Relations' direct-mail fund raising.

Carbaugh said the institute spent most of its money on publications. He said the institute also "took a number of surveys, and those things cost $15,000 to $20,000 apiece." Topic covered by the surveys, which Carbaugh said were conducted by Opinion Research Corp. in Princeton, N.J., included attitudes on the strategic arms limitation treaty, the Panama Canal treaties, human rights and "cartels, commodities and stockpiles."

Carbaugh said the Centre for a Free Society had "undertaken a number of projects which are basically in their formative statges." The group took in about $75,000 since November 1978.

He said the center had sent Dr. Alberto Piedra Martinez, a board member; on a trip to Guatemala, El Salvador and Honduras to meet with government leaders, in those countries and report back on "attitudes of the central American countries after the fall of the authoritarian government of [Arastasio] Somoza" in Nicaragua.

Carbaugh said that he had had a hand in founding all four of the non-profit foundations, which he said examine "root problems." He said all four are tax exempt.

He and Lucier both said they had traveled several times at the expense of the Institute of American Relations but could not recall traveling at the expense of the other organizations.

Helms said the tax-exempt groups grew from an idea he had when he first came to the Senate in January 1973.

"I realized that we [conservatives] had nothing to compare with the liberal think tanks." Helms said. When asked his connection with the foundations, Helms replied, "I just authorized it being done."

Carbaugh, Helms and Lucier all maintained that the organizations are financed by individual contributions from people in the United States. They said the foundations have never accepted foreign donations.

Helms also has traveled courtesy of the Institute of American Relations. He said he went to London in July to visit British Prime Minister Margaret Thatcher, and the institute paid for that trip.

Carbaugh said the institute had paid for trips by him to South America in 1976, Central America in 1977, West Germany in 1978 and South Africa and Zimbabwe-Rhodesia last August, plus the trip to London last week.

"In each case it was related to some issue that was current for which I wrote a report for the institute afterward," Carbaugh said.

Carbaugh said he had never received compensation other than expenses from any of the foundations, but his 1978 financial disclosure statement listed $2,034.57 for articles written for the Institute of American Relations.

Confronted with the statement, Carbaugh said the sum was actually expenses he incurred while working for the institute that he could not claim because "I didn't have the vouchers for it."

He said he reported it as income "to err on the safe side" and still was searching for the vouchers so he could recover tax paid on the money.

Lucier's disclosure statement listed a payment from the Institute of American Relations of $1,001 to $2,500 in 1978, and he said that on occasion he received other compensation from the institute.

Carbaugh's Senate salary in 1978 was $31,000; Lucier's was $39,835.41.