For an American in Britain these days, this is the time to encounter unaccustomed hope about the United States. It is a hope tempered with doubt, but Ronald Reagan's election has given a lift to English spirits. For the first time in a long while people here sense that the United States appears ready to cast aside the sort of brooding indecision that has characterized much of American actions in recent years and carve out a new, more resolute path for the future. Even Americans in London, including some operating in officials capacities as representatives of the Carter administration, apparently could not disguise their glee at the presidential results: guests at a U.S. Embassy election night party tells how cheers greeted the news of Reagan's quick and overwhelming triumph.

The aftermath inevitably brings more cautious appraisal. As a maitre'd at one of London's elegant restaurants put it the other day. "And what about that governor, sir? Were your people as surprised as we were? And do you think he's going to be up to it? I mean, he's not just going to be your governor, he's going to the the governor of the whole blooming world."

The British have a special reason to watch the advent of the age of Reagan even more closely than usual. Their own recent experience parallels that of the United States; and their experiment with dramatic political change after a period of sharp economic distress and feeling of national decline has by no means proven to be successful.

Maraget Thatcher's conservative reign of promised tough economic measures to reverse Britain's slide -- a regimen so often cited as a kind of governmental model for the Reagan approach to America's problems -- has fallen on difficult days. At the moment the news continues to be bad. As The Times noted the other morning, after it was reported that the nation's trade surplus, had reached an all-time record last month, Britain now leads the world in the speed and severity of its recession. This, in turn, has pushed down its imports and forced British companies to hold onto their export markets, and all despite a sharp increase in the value of the country's oil exports that same month.

An American finds striking similarities in the bitter political debates now heard in Britain and those that are virtually certain to occur at home once Reagan takes power. Here the government struggles with its promise to slash public spending drastically and also control the money supply -- and finds neither working. Here you find the government forced to retreat on making reductions in social security spending and facing the prospect of maintaining its professed economic strategy only by imposing heavy and unpopular increases in taxation. Here you encounter complaints about low productivity, profit erosions, high interest rates and continuing inflation. And here you sense a government retreating from its promise and torn by internal disputes over what course to pursue.

A nasty fight became public recently when remarks of the deputy general of the Confederation of British Industry led to resignations of five companies, all with strong Conservative Party links. Sir Terrence Beckett, in a speech to the group, bluntly criticized the government's economic policy. "You had better face the brutal fact, I think, that the Conservative Party in some ways is rather a narrow alliance," he said. "How many of them, let me ask you, in Parliament or in the Cabinet have actually run a business? Now this matters. They don't understand you . . . We've got to take the gloves off, and we're in a bare-knuckle fight on some of the things we've got to do."

All this, of course, strikes familiar chords in any American political observer -- particularly at a time when the British papers are filled with stories about the great plans for the new Reagan administration to cut deeply into the U. S. federal spending. The advice -- and it is entirely friendly -- to the Reagan camp from leading British financiers with whom I have had the opportunity to talk the past few days appears uniform: strike fast and hard with your boldest plans else forever forgo the opportunity to achieve truly major change in the way the government does business.

But that's not the only, nor the most important, hope for a Reagan America you hear expressed.

Perhaps the British, with their reverence of tradition and pride in continuity, see us in a special light, but their aspirations for America are no less relevant because of their perspective.In one way or another, people say they hope the Reagan presidency signals an end to the peiod in which the United States seems to have been stumbling, lurching and thrashing about in search of a purpose. Their hope is that the fragmentation, self-destruction and rejection of leader after leader that have characterized the last decade or so of American life will be replaced by a new one of stability, maturity and strong sense of national direction. The wish is hardly new, nor the diagnosis of American failings all that fresh.

Long ago Dickens defined a side of the American character that stands today all the more visible a problem. When he completed his memorable trip to the United States in 1842, he was struck by the many fine traits he had found among Americans everywhere, "They are, by nature, frank, brave, cordial, hospitable and affectionate," the great Boz said upon his departure. But he detected a darker side, what he called "the prolific parent of an innumerable brood of evils, Universal Distrust." Then, posing as the messenger, he said:

"You carry," says the stranger, "this jealousy and distrust into every transaction of public life. By repelling worthy men from your legislative asemblies, it has bred up a class of candidates for the suffrage, who, in their very act, disgrace your institutions and your people's choice. It has rendered you so fickle, and so given to change, that you inconstancy has passed into a proverb; for you no sooner set up an idol firmly than you are sure to pull it down and dash it into fragments . . . Any man who obtains a high place among, from the president downwards, may date his downfall from that moment."

To Dickens, the question was: "Is this well, think you, or likely to elevate the character of the governors or the governed among you?

Americans seldomed have answered that question satisfactorily since. Now, it becomes all the more critical for the success of the latest governor who will come to power in Washington.