HOPE AND GLORY: Britain 1900-1990.<i> By Peter Clarke</i> .<i> Allen Lane/Penguin: 480 pp., $29.95</i>

If, as President Clinton stressed in his inaugural address in January, the 20th century has been “the American century”--and nobody would argue with that--what sort of century has it been for Britain? The obvious answer is a century of painful, unremitting decline. And so it has been if a nation is to be judged on its ranking in an international league table of wealth and power.

“In 1900,” writes Peter Clarke in the prologue to the stimulating history “Hope and Glory,” “Britain was arguably the greatest power in the world.” But as the century proceeded, the three pillars of that power--the royal navy, the Empire and the gold standard--began to totter and then collapsed.

The century had hardly begun before the British government had to face the fact that its naval fleet could no longer compete with the United States’ fleet. By 1913, Germany, which in 1900 had produced 13% of world manufacturing output compared with nearly 19% in Britain, had reached 15%, and Britain’s share had fallen to less than 14% (while the United States was already approaching one-third of world manufacturing output).

The British Empire reached its greatest extent between the two world wars, when a quarter of the world’s surface was painted red on the map. But after World War II, it started to disintegrate--first, in 1947, with the loss of India, and then, from the end of the 1950s onward, with a great rush of independence in Africa, the West Indies and elsewhere. This summer, Hong Kong goes back to China, and the red on the map will be limited to a few incongruous little dots in places like Gibraltar, St. Helena and the Falkland Islands.

As for the totemic gold standard, which depended on Britain’s being able (as the saying went) to “look the dollar in the face,” it was suspended during World War I but restored by Winston Churchill as chancellor of the exchequer in 1925 against the strong advice of J. M. Keynes. With the pound sterling now grossly overvalued against the dollar at its historic level of $4.86, and with Britain no longer able to rule the waves of currency speculation any more than it could the sea, the pound was forced off the gold standard six years later, and its dollar value soon fell to around $3.40. (It is now about $1.60.)

In 1962, Dean Acheson made his still telling--and for that reason still resented--remark that Britain had “lost an empire and not yet found a role.” But does that mean that the 20th century has been an unmitigated failure from Britain’s point of view? Clarke, who is professor of modern British history at Cambridge University, doesn’t think so.

“This story cannot be simply told as one of decline,” he writes. “Though the laurels of international leadership passed to others during the 20th century, Britain still had its moments of glory, not all of them illusory; and Britons nourished hopes, not all of them misguided, that a condescending posterity should not dismiss but try to understand.”

Clinton’s inaugural address was reported with some irritation in Britain because he seemed to want to concede no aspect of 20th century achievement to any nation other than his own. Americans, he said, had “split the atom,” whereas every British schoolchild knows that the atom was first split in 1931 at the Cavendish Laboratory at Cambridge by the young British physicists John Cockroft and E.T.S. Walton.

Americans, added Clinton, had “invented the computer,” though Bill Gates, in his book “The Road Ahead,” says that “it is hard to sort out the paternity of the modern computer, because much of the thinking and work was done in the United States and Britain during World War II under the cloak of wartime secrecy.” Gates goes on to say that it was inspired by “visionary British mathematician” Charles Babbage in the 1830s and identifies Alan Turing, another “superlative Cambridge-trained British mathematician” working 100 years later, as one of “three major contributors” to the modern machine.

Although Clarke doesn’t make much of the fact, British achievements in science and engineering during the 20th century have been pretty remarkable, even if they have rarely been exploited to the nation’s benefit. Radio, television, penicillin, the jet engine, the communications satellite: These and many other modern wonders were invented or pioneered in Britain or by Britons in this century. Britain has been second only to the United States in its accumulation of Nobel Prizes for science.

But these achievements, as those in the arts, literature and popular culture, are no measure of a nation’s overall well-being, which nevertheless improved spectacularly, despite periodic setbacks. Whatever Great Britain’s economic and political decline has been by comparison with other nations, the 20th century has unquestionably brought the British people vast improvements in their living standards and general welfare, as it has to everyone else in the West. Ordinary working people today have far longer lives, much better health and enormously greater wealth than they did in 1900.

To take life expectancy alone, the death rate for males under 45 was six times higher in 1900 than in 1980 and, for women, 10 times higher. “In England and Wales in 1980, there were 12 deaths per thousand babies under the age of 12 months,” writes Clarke, “whereas in 1900 there had been 163--the sort of level which we now associate with the Third World.”

And even after World War II, which dramatically depleted Britain’s national assets, the improvement in living standards did not stop. On the contrary, it accelerated. Per capita gross domestic product grew by 35% in real terms between 1900 and 1948 but, between 1948 and 1990, it grew by 150%. The improvement in living standards was backed by major reforms in social welfare, which started early in the century but climaxed just after World War II with the Labor government’s creation of a National Health Service to provide free medical treatment for all.

For Clarke, the question is not whether Britain could have avoided its relative decline in this century--loss of world supremacy to the United States was always inevitable--but “whether the British people could in some way have done better, had they seized their historical opportunities by making different collective choices.” It is true that Britain would not have squandered so much wealth (let alone blood) if it had kept out of the two world wars, but one can hardly now regard its resistance to Nazi Germany, whatever its cost, as a mistake.

The biggest mistakes came after World War II. One was Britain’s refusal to stop behaving like a great power long after it should have known that the game was up, thus crippling itself pointlessly with huge expenditure on defense. The other was its failure to learn the lesson of 1956, when the emptiness of its imperial pretensions were brutally exposed by President Eisenhower, who used America’s financial muscle to force an end to the Franco-British invasion of Egypt.

France responded to this humiliation by seeking a new national destiny for itself in Europe, but Britain, consistent with its historical suspicion of close involvements with its continental neighbors, foolishly refused an invitation in 1956 to be one of the founding members of the European Economic Community.

Although it joined the community almost two decades later, Britain still cannot decide today on the kind of relationship it wants with Europe. Clarke ends his book by saying that the issues concerning Britain’s relationship with the European Union (as the changed EEC is now called) “can hardly remain unresolved into the twenty-first century.”

But why not? Commenting on the outrage provoked in Britain by his veto of its application to join the EEC in the 1960s, Gen. Charles de Gaulle feigned astonishment that he should be reproached for stating simply that Britain was an island. The fact that Britain is indeed an island, one inhabited by people with insular attitudes, has generally worked throughout history to its advantage. But perhaps that is no longer so.