ALISTAIR COOKE, who has spent his life explaining America to Britain and his native land to his adopted country, presided over an informal debate last month over whether the United States needs a ministry of culture. "Sponsorship of the arts in the U.S. has been overwhelmingly private," Cooke said then, "and don't think this is a very bad thing." The question came up to an Arts International meeting on exporting U.S. culture.

In fact, the first U.S. efforts at using actors as ambassadors were under private sponsorship. They go back to 1949, when a native of Independence, Mo., sought the help of a boyhood friend who had become president of the United States.

Starting out as a schoolteacher, Blevins Davis had switched to radio, where he instituted Friday afternoon's "Theater of the Air" on NBC. So welcome was the program that the last period of the school week became an hour of cultural education piped into classrooms from the Atlantic to Pacific.

When his bride of a few weeks died on their wedding trip in a private railway car, Davis had inherited her fortune, enabling him to become an investing producer for theatrical ventures. In time his generous enthusiasms would stretch from Howard University to Moscow, from Ballet Theater to Colorado's Cripple Creek Gazette. Davis would die close to broke but gloriously proud.

Upbeat and accessible, Davis was the man to whom a State Department official turned when seeking an American company to perform "Hamlet" in Elsinor's Kronborg Castle. British, French and German players had set a precedent pleasing to Denmark's tourist trade, and the Danes wanted an American troupe.

The official sent the Danish request to the governor of Virginia with the suggestion that, since his was the only state contributing to a theater company, the Barter Theater, perhaps its director, Robert Porterfield, could implement the request.

The Barter's current production was, indeed, a "Hamlet" with the young, quite unknown Hume Cronyn in the title part. Porterfield formed an alliance with the revived American National Theater and Academy (ANTA) project. Aware that Cronyn did not wish to continue in the role, Porterfield approached John Garfield.

Blevins Davis, a member of the ANTA board, paid all the bills. Important as his money was to this early exchange program, his boyhood friendship with both Trumans was more so. The White House smoothed the way.

Davis next backed a tour by the Howard University Players in Ibsen's "The Wild Duck." In time he would back Ballet Theater for its early overseas tours and ultimately would pour a fortune into Robert Breen's brilliant, never equaled revival of "Porgy and Bess," which introduced Leontyne Price and William Warfield.

Though the Truman recognition of such international exchange remained entirely unofficial, by the time of "Porgy and Bess," the Eisenhower administration had created an official slot and budget for such ventures. The State Department would get $2.5 million a year for its cultural exchange program.

An advisory panel was created to "suggest" particular plays and players to the State Department. A few such schemes came to fruition, notably a repertory company in "The Skin of Our Teeth," "The Miracle Worker" and "The Glass Menagerie" headed by Helen Hayes, Mary Martin, George Abbott and Eileen Brennan.

But problems arose. A few congressional figures questioned choice of plays or performers; some pushed for mediocre, home-district talents. Because they were deemed controversial, such dramatists as Arthur Miller and Lillian Hellman were shunted aside.

Even "Porgy and Bess" couldn't get its cast from Berlin to Moscow through government funds. The timid spirits at State cautioned that "Porgy" portrayed blacks as dope addicts and, even, that the anti-Semitic Soviets would not appreciate work by George and Ira Gershwin.

Disheartening as this was, professionals in the field have taken part. Washington's Arena Stage, San Francisco's American Conservatory Theater, SUNY's children's theater and other admired groups have made tours for the program, as have individual performers and playwrights.

Governmental practice of sending artists abroad sometimes has been taken over by USIA, the United States Information Agency--sometimes as a part of State, sometimes as an independent agency.

USIA's exhibit, "American Theatre Today," attracted more than 127,000 visitors to Budapest's Mucsarnok Art Gallery last year and will tour further in Eastern Europe.

In sum, the cultural exchange theater program, when it has flourished, did so through strongly determined professionals and with the backing of private, wealthy enthusiasts. But for most of its years it has had to settle for modest ventures more likely to reflect than to display the American dramatic arts.

And you never know where matters may tumble. There once was a congressional uproar over exporting "The Grapes of Wrath" to Poland in the '50s. When the exchange finally was achieved, what impressed the Poles was that unemployed Americans were looking for jobs in their own automobiles.