John Jeffrey Louis Jr., the United States ambassador to the Court of St. James's (or Britain, as mere commoners call it) is the affable incarnation of a purely- political appointee, an "amateur" in public life, as he freely admits.

He enjoys shooting, golf, the "thrill" of bringing British notables to his residence -- something he does constantly -- and presides over the sprawling 800-employe embassy as "chairman in the midst of policy discussion and decision." He is emphatically not an operational diplomat, given to writing expert cables or shaping American positions. He doesn't know enough about the issues, nor does he claim to.

It is a truism about the way international relations are conducted in the jet age that ambassadors are not what they used to be, diminished in influence by the instant communications among world leaders and the use of globetrotting special envoys, like Philip Habib in the Middle East. But not all ambassadors are figureheads. Former Federal Reserve Board Chairman Arthur Burns in Germany and long-time Senate Majority Leader Mike Mansfield in Japan are two eminent senior figures whose advice and counsel as ambassadors have been highly regarded by both their hosts and the governments at home.

In hot spots like El Salvador, Poland or Israel, ambassadors, (who in those cases are career diplomats) are deeply involved in the implementation of sensitive American policies that require daily, on-the-ground supervision.

Even if Louis wanted to expend more energy on such matters, it is doubtful he would have the time. He and his wife Josephine are maintaining a social schedule -- "representational events" in the official jargon -- that is the most elaborate in Britain, with the possible exception of members of the royal family. In November, for example, the Louis' staged 22 scheduled lunches, dinners and large receptions.

In one typical week, they were busy every night including Sunday (dinner for visiting USIA director Charles Z. Wick), attending, among other things, an American Airlines dinner, a Pilgrims Society dinner and a dinner for the American Banks Association in London. Recently, they had 50 people in for Prince Charles and Princess Diana, among them Julie Nixon and David Eisenhower, who flew over for the event. The queen came last month to meet a table full of top American businessmen.

Clearly, in the continuing dabate about how may ambassadorships should be given to political appointees, -- about 30 percent have been in the Reagan administration -- Louis' is a classic case. His is the story of what happens when a highly visible, active post is filled by an untutored businessman, a man who is by any measure save his waistline, a fat cat.

"I will never be a professional," Louis said in an interview, speaking in a soothing, soft voice, with a manner that manages to be both disarmingly open and consistently distant. "People get to be that way by spending their lifetimes in this business." In his 57 years, being ambassador to Britain is the "most exhilirating thing that has ever happened."

Given Louis' bland past, that would not be difficult, some have suggested. Malcolm Toon, a retired senior career diplomat, wrote acerbically of Louis last spring. He owes his "place in life to the fact that his parents founded a furniture-polish dynasty (Johnson's Wax)," Toon wrote, and his only qualification for the London post "is that he speaks English." He is undeniably a Johnson scion on his mother's side. And his English is impeccable.

The Wall Street Journal, in a lengthy profile at the time of his appointment that Louis says left him "deeply upset," termed the new envoy a practioner of "checkbook politics" and, it strongly implied, little else of consequence. Quoting, "a friend," the Journal spoke of Louis' "retirement at age 32." In 1972, the paper said, Louis gave nearly $300,000 to Richard Nixon's campaign, making him a leading contributor.

By his own account, Louis has spent most of his adult life as a "venture capitalist" in the Chicago area, investing primarily in other peoples' businesses and serving on various boards of directors or supporting philanthropic organizations. His only foreign experience came in the late 1950s when he worked in international marketing for S.C. Johnson & Son, the family firm.

The ambassador acknowledges that he had a great deal to learn when Reagan tapped him for Britain after an introduction during a New Year's 1980 weekend in the luxury of Palm Springs. The meeting was engineered by Walter J. Annenberg, Nixon's ambassador to London and a business magnate to make Louis look like a piker.

As Louis described the episode to The New Yorker last March, he and his wife spent "three very pleasant days" with the Annenbergs, Reagans and others in the "kitchen cabinet" "playing golf, watching the Rose Bowl and having dinners in the area." On Jan. 2, Reagan called Louis and said, "I'm at the point, John, where I would like to suggest to you that I am considering asking if you would represent me in Great Britain." Louis said he stuttered a bit and then said, "I would consider that the highest compliment and, of course, we would love to consider it if you think I'm qualified."

He said, "You're qualified."

Louis says he was nine months into the London job before he was "up to speed" with all the alphabet soup of bureaucratic initials -- CSCE, MBFR, GATT, INF -- that are the lingua franca of American diplomacy. Even today, 18 months after arriving here, he says he feels only "80 percent" confident in talking about "most of those things that are going on in the world." He still keeps a list of official abbreviations on his desk, "so I can look up the odd one," he added.

Perhaps most embarrassing of all, when Argentina invaded the Falkland Islands last April 2, precipitating the most serious foreign policy crisis for Britain in decades, Louis was vacationing in Florida. He did not return to London until April 11, after Secretary of State Haig had begun his fruitless transatlantic shuttle. Louis says he was in touch with the embassy daily by telephone and made an effort to get back as speedily as possible. But he is fuzzy in explaining why the return took so long. Embassy officials, who as a group seem protective of Louis because they genuinely like him, now believe that for his own good they should have catapulted him back to London immediately -- although the course of the crisis, they concede, would not have been changed.

So is John J. Louis Jr. a successful U.S. ambassador to Britain? On the way to his office each morning, as he passes the portraits of his celebrated 20th-century predecessors, people like W. Averill Harriman, John Hay Whitney, David Bruce and Kingman Brewster, can he walk tall? (Most, incidentally, were political appointees, but with glittering resumes of public accomplishment.)

Bruce, who served in London from 1961 to 1969, and later was negotiator for the Vietnam peace talks and the first American envoy to Communist China, was able to call on decades of experience in watching Europe for the administrations he represented. Kingman Brewster, a former president of Yale, who was Louis' predeccesor, played an active part in the London negotiations to bring majority rule to Rhodesia.

Louis says he doesn't know enough about Bruce's or Brewster's tenure to compare himself to them. Measured in his own terms he doesn't yet know how well he's doing. For a large, silver-haired man, in ambassadorial uniform of navy blue suit, and striped shirt with collar pin, he still manages to seem earnestly boyish.

"I miss the concrete tangible benchmark of performance that businessmen have which is the profit and loss statement on the balance sheet," he said, "but as far as what has happened to me here, I have been twisted and stretched and72, challenged. . . . I am satisfied with myself in that I took the risk and gamble of jumping into something I knew nothing about, something which shook me rather severely when I first made the decision."

British politicians, officials and diplomats -- including one at a very high level in the Thatcher government -- take a friendly view toward Louis and his embassy. There is , for instance, no condescension of the type that bedeviled Annenberg , whose syntax in interviews and grandiosity in taste were picked apart here. On the other hand, it is widely accepterd that on policy questions, the British government can -- and does -- deal smoothly with the U.S. administration through the embassy in Washington under Sir Oliver Wright, a career diplomat, rather than circuitously through the American Embassy here.

Wright, who had just retired from the Foreign Office when he was recalled to go to Washington -- the British version of a political appointment -- and his predecessor, Sir Nicholas Henderson, with the same background, have been socially prominent in Washington. But they also need to be adept at policy: Wright in bargaining over an end to the dispute about Reagan's sanctions for British companies supplying equipment for the Soviet natural gas pipeline and Henderson during the Falklands where he became a peripatetic salesman of the British position.

To handle the myriad aspects of Anglo- American relationships locally (there are dozens of U.S. agencies represented in London, engaged in probably the most extensive collaboration the United States has with any country in the world), Louis relies heavily on his deputy chief of mission, Edward J. Steator, a career diplomat who has been in London for nearly six years. StreaTor gets high marks from the British for his contacts and knowledge of the British scene -- and for seeing to it that the ambassador says and does what he should. Louis calls him the embassy's "chief operating officer" and it is widely known in London that it is Streator who keeps things running.

"If Streator or someone like him didn't exist, there would be a serious problem when it came to substance," one candid senior British diplomat said, "but he does. Louis is not deep, but he doesn't pretend to be. And the social settings provide an important meeting place, a chance for others in the embassy to meet with all kinds of people and talk. As a result, the United States' is the best plugged- in embassy in London."

Louis does have some political views, of course, and expresses them to the endless stream of Ameican official visitors. "If he has (Secretary of State)Shultz to himself in a car or at lunch and tells him what he thinks is going on in Britain, that can have an impact," said one official. The ambassador is cautious enough to make sure those opinions reflect mainstream Reagan administration attitudes on, say, economics or defense and are based on the best estimates of his staff.

But in the main, the ambassador seems to have settled into the role for which he is most suited: a dispenser of good will and good times. Louis and, he says, especially his wife, have come to thrive on the pace of entertaining, although it can be exhausting. "There were times early in my tour when I wondered whether I was going to be able to bear up," he said; now the Louis wonder how "we are going to unwind when the dreadful day comes that we have to go and do something else."

With a sizable social secretarial and management staff, an annual embassy entertainment budget of $130,000 (undoubtedly supplemented by Louis, diplomats believe), wining and dining in London is a major undertaking. From the way it looks, much of it is probably more tedious than fun. At big receptions like July 4, Louis essentially functions almost as a maitre'd would, standing at the door greeting guests and moving them swiftly into the maelstrom.

Nearly every function in the elegant Georgian-style ambassadorial residence, Winfield House, has a purpose. Members of the Trade Unions Congress got a Western-style barbecue last summer, the Labor Party politicians got after-dinner entertainment with selections from the musical "Oklahoma!" Prince Charles and Princess Diana were provided an astronaut, a Harvard philosopher and his fiance, a psychiatrist at the National Institutes of Mental Health and a California computer whiz (Diana also asked that a few of her young pals be invited and they were).

When Jimmy Carter came to London recently promoting his new book, Ronald Reagan's ambassador gave him lunch, just the two couples. Margaret Thatcher was provided a room full of selected Americans resident in London.( She sat next to the writer Paul Theroux, who describes her unattractively in his next book, saying, "Even her hair looked hard."). In short, the Winfield House premises are a revolving door of British and American people of considerable range.

"A good salesman doesn't do his best work if all he does is make office calls," said Louis; "the way to get close to people is to put them in informal settings."

Louis says that before important occasions he worries about keeping conversations going, "the way an actor feels before going on stage." In its way, its an appropriate analogy for Ambassador Louis to make. Whatever else he may be doing in London on behalf of the government of the United States, he is definitely on show.