WHEN members of Parliament enter the Victorian majesty of the Palace of Westminster, with its two miles of corridors and 1,180 rooms, they hurry past the polished oak, the gold leaf, and the colorful coats of arms to one of the few areas of less than baronial splendor.
There they find waiting for their coats plain, utilitarian hangers. From each is suspended a length of red tape.
For umbrellas? Documents? No - the tapes have hung there for as long as anyone can remember so that, before proceeding to the floor, members may hang up their swords.
Decorated hilts and scabbards may have faded, but their memories linger on. Both the tapes and the palace itself (completed in 1852) are reminders of an imperial age, when Britain's rule extended so far around the world that the sun could never set on it.
Like the swords, the empire has vanished, but its memory and influence remain - in society, in institutions, and in individual attitudes.
Politicians might clash daily on the pace and depth of current economic recovery, and on the standing of Prime Minister Margaret Thatcher, but the empire, which in historical terms ended a short time ago, bequeathed a remarkable, underlying legacy:
A world view symbolized today by the Commonwealth; a competent central bureaucracy; skilled military forces; preeminence in banking and finance; and a tradition of elite, quality boarding schools which educated the children of far-flung colonial administrators and, in turn, provided the next generation of officers and officials. The empire also helped foster the kind of professionalism in the spoken word that created the BBC (whose World Service began in 1932 primarily as a way to link the countries of the empire).
There are other, sometimes less desirable legacies:
A hierarchical society that tends to be deferential in face of rank or title; an unwillingness or inability to see that the British need above all new social attitudes to help them rediscover in themselves what John Rae, the headmaster of Westminster School in London, describes as ''those national characteristics of energy, aggression, and enterprise that had once made their island the most successful trading state in the world.''
The good qualities can also seem obscured by the divisive public debate that goes on here day by day, centering largely on economic statistics and how much influence the central government should gain or lose.
The political system is a sharply adversary one. The public debate is shrill and often cast in personal terms. The public is helped by excellent radio, some good television, and some high-quality national newspapers. But most of the overmanned, technologically backward Fleet Street press battles for circulation using the weapons of trivia, sensationalism, and emotionalism.
The beneficial legacy of empire, however, remains substantial. The question is whether it is enough to transform Britain into a more flexible, forward-looking, prosperous state.
Many outsiders have the impression that, in general, this country is an old-fashioned place, pleasant to visit but emptied of real power, filled with public figures intoning the kind of statement heard in the House of Commons recently - ''Mr. Speaker, sir, I am all in favor of progress - as long as it doesn't mean change.''
Often Britain attracts attention because of its past instead of its future, because of its royal pageantry, its military parade grounds, its picture-postcard countryside, its historic buildings, its dukes and its earls.
Britain still is challenged to give a full and satisfying answer to the observation made by Dean Acheson, former US secretary of state, not long after this country's superb stand against Hitler. The British had lost an empire, Mr. Acheson commented, but not yet found a role.
The ebbing away of global power has left once-great institutions shadows of their former selves. Change rushes in on all sides, not always fully understood, often uncomfortable and sharp. Among the most difficult to deal with: the 16 percent unemployment rate among the 71/2 million Britons between the ages of 16 and 24 - young people with a bare minimum of education, few if any skills, and the feeling they have no future.
YET the past is Britain's strength as well as its weakness - provided it can maintain stability without impeding progress.
A foreigner living here, studying the imperfect mirror of the daily press, hearing the constant self-deprecation of the British people, goes through several stages.
First, there is the temptation to see Britain as one of those clanking ceremonial swords: a charming anachronism rather than a modern cutting edge.
Second, comes the recognition that this country, with its centuries of courage and religious conviction which gave the world the King James Version of the Bible, has the potential to accept and generate needed change more and more quickly.
Third, is a growing awareness of two other ''Britains'' and their assets.
One of these Britains is the civilized heir to empire, the inaugurator of the first Industrial Revolution. The second is the country struggling to adapt to the second industrial revolution of microchip and service industries - to make the transition from steel and textile plants to leaner, more efficient factories , to develop more computer software, to sharpen and expand already formidable financial skills, to continue a traditional mastery of communications.
But is this second Britain adapting fast enough?
It is not easy to tell, and the verdict is not yet in.
Inflation has dropped, but the national unemployment rate (unadjusted) in February 1984 had reached tragic proportions: 13.4 percent, or 3,186,386 individuals.
Too many roads, railroads, telephones, water and sewage pipes, public housing and schools suffer from lack of investment and repair.
The economic gap between the north and south of Britain grows more marked. Northern England, Scotland, and Wales have more people out of work, and the region is growing relatively poorer. Southeast and southwest England have jobs, money, cars, prospects.
Central governments keep raising indirect taxes - such as those on tobacco and petrol - as well as charges for gas, electricity, and health prescriptions while cutting funds for universities, the arts, and local government.
YET life here retains a quality, a flavor, a taste, that attracts. People display qualities of calmness, poise, humor, helpfulness, stability, even in the teeth of economic adversity.
Unemployment is an epidemic - as high as 50 per-cent among young people in some areas of the north - but the social welfare net is extensive. Total benefits for the unemployed can amount to 90 percent or more of the lowest blue-collar salaries.
And, as the old industry of steel plants and coal mines offer fewer and fewer jobs, newer ideas do begin to appear:
* One of the less-publicized long-term policies of Prime Minister Thatcher, for instance, is to put a microcomputer into every state-run high school in the country. History may remember her more for this than for the Falklands victory or her economic reforms. British programmers are in demand throughout Europe.
* To survive recession, Scotland has attracted many overseas companies to its own ''silicon glen.'' Northern Ireland and Wales also compete for microchip light industry with some success.
* Some of Britain's fastest growth is in the so-called western corridor, roughly bounded by the M40 and M3 motorways which flank the jampacked M4 and include urban areas from Uxbridge and Hounslow westward through Slough, Reading, and Newbury out to Swindon and Bristol. A new study by the Policy Studies Institute suggests that job losses caused by computers replacing people in manufacturing so far are strikingly small.
* Sir Clive Sinclair has invented a cheap microcom-puter for the home, as well as a low-priced, high-powered micro for business, a pocket television with a two-inch tube, and what he describes as a cheap aerial for receiving television programs direct from satellites in space.
* Television viewers whose sets are equipped with the Teletext and Oracle data system can, at the touch of a key pad, bring into their homes an array of news and information that astonishes visiting Americans.
Meanwhile, the ability of militant trade unionists to bring industry to a standstill is gradually being eroded, despite recent headlines about a miners' strike. Restrictive demarcation rules are being blurred: Tradesmen drive cranes, workers service machinery.
The microchip is blurring the line between white- and blue-collar work. In electronics and robotic factories, a new breed of ''craftician'' is emerging.
OUTPUT per worker is up: In the first quarter of 1983, the British steel industry claimed production of 230 tons per employee, 15 tons ahead of West Germans.
In Coventry, a new type of manager is symbolized by blunt-spoken John Egan, a stocky Lancastrian with experience of North American business methods. Mr. Egan has shown what can be done to brush up the British image of quality.
He has turned the Jaguar car company around. He has reduced the work force, kept it informed of weekly sales figures, emphasized quality, changed suppliers, set up staff ''quality circles'' to work on specific problems - and seen production and profits rise beyond expectation.
Britain has other assets as well.
''We are self-sufficient in energy, in oil, coal, and gas,'' said the Speaker of the House of Commons, Bernard Weatherill, in a recent interview.
''We are a member of the Common Market. We have a special relationship with the United States. We have the Commonwealth. It is often underrated, but it is more than 40 countries sharing a common language and set of traditions, a kind of United Nations in miniature. . . .
''I don't think we will ever be a world power again, but we can be an enormous world influence. . . . The future of our country should be as a quality nation with high-quality people having high-quality ideals, making high-quality products.''
Many Britons, lower and middle and upper class alike, wholeheartedly agree. Yes, they criticize their own country, but they still believe that on the whole, it does remain a bastion of civilized stability. They see it as a center of excellence in fields ranging from theater to radio and television, in music (classical and pop), clothes and fashion, in education, the arts, and dance.
Even the famous class patterns are changing. As blue-collar work declines, white-collar work grows and the middle-class and its values spread.
The City of London shows British leadership in finance, in share and commodity dealing, in accountancy, corporate counseling, banking, insurance.
Tradition both sells and appeals: Two million Americans came here as tourists in 1983, up 34 percent from 1982, and seemed generally happy with what they saw and did. They mingled with 5 1/2 million other tourists.
Millions of families go for comfortable Sunday afternoon drives and walks through parks and fields and return to afternoon tea.
Secondary schools and universities, though healvily criticized here by the left wing as elitist and too narrowly academic, remain a jewel in the British crown.
The standard of living as measured by consumer gadgets grows - even, surprisingly, for many of those 3 million without jobs, and the 6 million or so family members affected by their plight.
But after listing the assets, the question remains: How long can it all last if the country's industry, and thus its exports, don't show marked improvement soon?
No one knows, but it would be unwise to ignore ominous signs ahead. This is a centralized country. More of society depends on central government money than is the case in the US. What will happen if the growth of government income begins to drop?
The production of North Sea oil and gas, for instance, is set to decline before 1990. In 1982, total oil andgas production repesented 5 percent of the gross national product. One-quarter of all UK industrial investment went on the North Sea. In the City of London one estimate is that combined oil and gas taxes will rise to $:14 billion by 1987, then fall as production begins to drop. Much depends on future discoveries. Remaining reserves will be extensive and difficult to extract.
Britain will need all its long-tested trading and industrial skills to make up for this loss.