It is some years now since the sun finally set on the British Empire. And yet, in one respect this country still does rule the waves--the air waves. The British Broadcasting Corp.'s External Services, with more than 100 million listeners around the world, has achieved a reputation for political independence and reliability that gives it a stature no other national radio can match.

With the Reagan administration and Congress casting around for ambitious and expensive new programs designed to promote democracy abroad, the BBC's unique international role as "an upholder of the values of free societies," as one of its former chairmen put it, bears a close-up look.

Over 50 years, mainly from its institutionally drab headquarters at Bush House in central London, the External Services (also known as the World Service, the name of its English-language program), has been putting out a round-the-clock stream of news and analysis, top-flight drama, music and even quiz shows. Once it was undisputedly dominant, but its strength today is quality, not size. Such direct competitors as the Voice of America and Radio Moscow are already better off financially and growing all the time.

The Soviets are believed to spend more than the BBC's entire annual budget to jam Britain's broadcasts to Eastern Europe. Radio Moscow now broadcasts over 2,000 hours a week in 84 languages. The VOA is on the air for just under 2,000 hours in 47 languages. By contrast, the BBC puts out only 730 broadcasting hours in 37 languages.

Indeed, for all its international prestige, economic stringency poses a serious continuing problem for the BBC and inevitably bears on its standing. Last week, for the eighth time in 10 years, the External Services' budget was earmarked for cuts. Auditors proposed taking out nearly $2 million of a total of about $120 million, enough to threaten the future of one language service and force delays in needed technical improvements, according to BBC officials.

In the last round, three language services were lost, but four others were spared because of the public outcry.

Political supporters of the service across party lines are again bound to put up a determined fight by arguing that the BBC is, as one Conservative member of Parliament put it, "one of the most important arms" of British diplomacy. The case could be made even more strongly. The BBC is perhaps the greatest single asset today to Britain's lingering image as a major world power, the authoritative voice of a mature nation with far fewer vested interests than it once had.

"England without the BBC," Tehran radio once said, "is a lion without mane or tail whose funeral will soon be due."

The impact of radio today is immense. As a result of transistors, there are radios in even the most remote corners of the planet: an estimated 1.5 billion of them, six times as many as in the mid-1950s. This represents the most direct means available of reaching vast numbers of people on a regular basis. The very fact that the BBC is not perceived as a superpower's advocate enhances its credibility.

In an age of advanced information technologies, of cable, satellites and teletext, the BBC remains old-fashioned in the style of its news broadcasts and only lately has begun switching to new forms of transmission. Nonetheless, its signal straddles the globe and is listened to faithfully by presidents and peasants whatever their political conviction.

The BBC's audience research staff says that people of widely divergent views listen because they regard the information as more likely to be true than what they can get elsewhere. "We are not an ideological service," Douglas Muggeridge, the present managing director of the External Services says, explaining a key component of its appeal. "We are not a government agency."

That opinion is even held among U.S. listeners. Kenneth Tomlinson, the new head of the VOA, wrote earlier this year of how two American political figures, a Democrat and a Republican, had approached him to express their concern over his plans for the American radio.

"I found," he recalled, "that the two agreed on one important point. Both confessed that when abroad they listen to the BBC, not VOA. Each declared the BBC's programing was far more informative, far more relevant. . . "

The BBC is, in fact, the incarnation of what Vladimir Lenin, the first Soviet leader, said international radio could be: "a newspaper without paper and without frontiers." Doubtless, Lenin's notion assumed tight state management of the contents. In Britain, the government's (and ultimately Parliament's) control of the purse strings is plainly a factor in how the radio functions, and the Foreign Office determines how much air time each language should receive.

But when it comes to the crucial matter of substance, daily judgments are always made by journalists who guard their sovereignty zealously.

During the Suez crisis in 1956, prime minister Anthony Eden all but ordered the BBC to reflect the government line and placed a Foreign Office representative on the premises. He was ignored. In more recent years, aside from predictable critics such as the Soviet Union and its allies, there have been complaints of bias from people like the late shah of Iran, who believed the BBC was instrumental in his downfall, and Indian Prime Minister Indira Gandhi, who expelled the BBC's New Delhi correspondent as practically her first act after she suspended the country's democratic rule in 1975.

In last year's Falklands war, broadcasting to Latin America was increased, but Prime Minister Margaret Thatcher's government made no direct effort to interfere in the contents. Instead, it set up a separate propaganda service "commandeering," in Muggeridge's critical account, a BBC transmitter on Ascension Island in the mid-Atlantic.

Tension plainly did exist during the conflict. "The Ministry of Defense knew it couldn't rely on the BBC in the war and didn't like that," said a journalist working at Bush House. There were complaints in Parliament about insufficient loyalty in both domestic and foreign services, but no retaliation was tried.

"Successive governments have recognized the value of editorial independence," said Muggeridge, who has been director for the past two years, capping a career in the BBC that began as a journalist.

Almost as important as credibility to the BBC is the ability of its broadcasters. Competition for jobs is intense, among both British aspirants and those abroad who hope to work in the various language services. Kailash Budhwar, now editor of the Hindi service, which is on the air 14 hours a week, was recruited by the BBC in India from, he said, "thousands of applicants."

Editors like Budhwar have considerable leeway in designing programs, to emphasize subjects of interest to their listeners. But the all-important news and current affairs material is supervised by English-language journalists to ensure that the contents are uniform throughout the services. A large central newsroom operates along the lines of other leading broadcast operations, except, interestingly, that reporters talk out their stories rather than write them down to make sure that they will sound well.

The External Services has its own staff and bureaucracy, separate from those working for the domestic service. But news resources are pooled, giving the overseas programs access, for instance, to 20 first-rate correspondents around the world. Their reports are supplemented by the opinions of academic specialists, foreign journalists and political figures who are interviewed in tightly packaged segments on issues of the day. The result is that the BBC can boast extraordinary breadth and depth.

For all its acclaim abroad, the External Services suffered a bit at home in the past by not being heard. As Britain's world responsibilities have diminished, some critics have said the BBC should be scaled back as an unnecessary luxury. Several years ago, because of what engineers termed "leakage" from transmitters, World Service programs started turning up clearly on regular medium-wave bands, especially in London.

BBC executives deny--although with a notable lack of vehemence--that this was a deliberate effort to build a constituency in Britain as devoted to the programs as those around the globe. Although no figures are kept, there is no doubt that many thousands of people here now listen to the World Service, including leading politicians. Their support will be tested in the coming budget fracas.

Whatever happens, Muggeridge said, the BBC will continue to follow the axiom that has always been the core of its philosophy: "Credibility is all."