Since 1954, Britain's increasingly important and, until recently, most secret intelligence agency--known simply as the Government Communications Headquarters--has been nestled against a hillside in this picturesque country town, a one-time spa that is a popular home for retired Army officers.

From its fenced compound of squat, nondescript whitewashed and brick buildings on the otherwise residential Prior's Road, Government Communications Headquarters oversees an elaborate global network of listening stations and devices. These perform highly sensitive electronic espionage work that the U.S. and British governments now fear has been undermined for years by an alleged Soviet spy named Geoffrey Arthur Prime.

The Prime affair has drawn an unwelcome spotlight to the activities of Government Communications Headquarters, a beam that may shine even more brightly when he comes to trial late next month for suspected violations of Britain's Official Secrets Act.

Notoriety is a new experience for the agency. Until the mid-1970s, Government Communications Headquarters was almost completely unknown, obscured by its bland name, the seemingly technical nature of its work and an official policy of deception.

"If asked, we said we worked at a government center into research on communications and its application to computers," one former long-time employe said in an interview.

Even today, relatively little is known about the details of what Government Communications Headquarters does, let alone the exact size of its budget, its work force or its cooperative relationship with other intelligence organizations here or elsewhere in the West. As a result, precisely what Prime was supposed to have turned over to the Soviets is a matter of dispute. But British and U.S. officials have conceded that the alleged breach of security at Cheltenham was "serious."

By focusing attention on Government Communications Headquarters--and, inevitably, on its bigger U.S. counterpart, the National Security Agency -- the Prime case also underscores the extent to which "sigint," or signals intelligence, has replaced "humint", or human intelligence, as the prime source of Western information about what other governments are doing. Experts say signals intelligence now accounts for about 85 percent of usable intelligence material.

The agency emphatically denies entry to journalists. But a portrait of it emerges from conversations with people who have worked there and from the writing of Duncan Campbell of the weekly political magzine, the New Statesman. Campbell has made a specialty of reporting on the British intelligence establishment and is called "very reliable" by sources with first-hand knowledge of the headquarters operations.

For all the trappings of secrecy and hints of glamorous danger that go with intelligence work, the principal function of the agency appears to be extremely tedious. The key staff among its estimated 6,000 employes in Cheltenham are the translators, like Prime, who sift the outpouring of raw data. The information is amassed by technology so sophisticated that barely a whisper anywhere is missed.

From all accounts, they lead workaday white-collar lives. Senior translators are paid about $15,300, and are classified as ordinary civil servants. Not long ago, along with other government staffers, they went on strike for better pay. In the past, many were hired from the armed forces (Prime was one of these) or Britain's colonial services. Today, most are recruited from universities.

"The translators are becoming more conventional now," a veteran employe said. "The entry procedure is more formalized. There used to be a lot of oddballs, anybody who had picked up weird bits of expertise or language."

Under a long-standing arrangement with the NSA in Washington, Australia's Defense Signals Division and Canada's Communications Branch of the National Research Council, the British concentrate on analysis of signals intercepted in Eastern Europe, the European part of the Soviet Union, the Middle East and Africa.

According to an operations chart obtained by Campbell and published yesterday in the New Statesman, there are four divisions within the "Directorate of Sigint Operations and Requirements." Division "J," where Prime, a Russian-language specialist, worked, is classified as "Special Sigint" and deals exclusively with the Soviet Bloc. The "K" division handles all other geographic areas, apparently with considerable specialization.

The "H" division is concerned with deciphering codes. During World War II, teams of U.S. and British code-breakers scored considerable successes in breaking German and Japanese codes. Their techniques were said to be the forerunner of the ones used by Government Communications Headquarters today, although the most advanced computer technology is now also used.

"Z" division is responsible for obtaining orders for intelligence material from British or other NATO governments and shaping those requirements into tasks for the monitoring stations and translators. Tracking Soviet military movements near the Iranian border through radio transmissions would be one such order.

Once scrutinized, the data is distributed to the supervisory intelligence committees who produce the final judgments on how it should be interpreted. British liaison officers are stationed at NSA's headquarters in Fort Meade, Md., and in Ottawa and Melbourne.

Prime worked at Government Communications Headquarters for nine years and is alleged to have been spying for the Soviets throughout that period. The primary damage he could have done, according to knowledgeable British sources, would be to tell the Soviets what the headquarters was hearing and how it was obtained.

Nonetheless, the mere possibility of any security breach is a source of great concern in Britain's intelligence community. The agency--whose secret budget is estimated at 300 million pounds, about $500 million--represents the core of Britain's intelligence effort. The worldwide total of its employes is thought to be about 20,000.

According to the Financial Times newspaper, the combined budget and resources for the other British intelligence agencies -- the Security Service, known as MI5, and the Secret Intelligence Service, MI6 -- is only about a quarter of that for Government Communications Headquarters.

Security procedures at Cheltenham are ostensibly being tightened. But entry to the base for employes still seems a routine matter of flashing an identification picture at a civilian guard who waves carloads of employes through without what appears to be much scrutiny.

More important than access to the installation are the security clearances for employes, known in the British jargon as "positive vetting." As it stands, according to intelligence sources, there are periodic reviews which include interviews, a detailed questionnaire on all habits and hobbies and a requirement to produce two references.

But no matter how extensive the examinations are, no matter how rigorous the checks, one source said, "there is no such thing as complete protection. That's something every intelligence agency has to face. There will always be espionage."