As the British see it, the outcome of the mid-term U.S. election could well determine the viability of Ronald Reagan's presidency. And for Prime Minister Margaret Thatcher's government, the best result would be, as one official put it, "continuity and consistency."

Despite the differences over supplies for the Soviet natural gas pipeline, steel and other trade issues, Thatcher is a staunch Reagan friend.

"Ronald Reagan is obviously not going to impress the left in this country or anywhere else," one Downing Street source said, "but the majority opinion would see him as a more, rather than less, reliable partner, and that he is on the right side when it counts most."

The central issue here and in many other European capitals, is whether a strong American president--even one whose policies are considered seriously flawed -- is preferable to one that, in the words of one observer is broken, "limp and twisting in the the wind for two anxiety-ridden years."

The dangers, or alternatively, the opportunities of that prospect were raised this week in the Guardian newspaper, a critic of Reagan's economic and defense strategies. A clear repudiation of Reagan, combined with the reasonable possibility that he will not run for a second term because of his age, would effectively collapse the president's power, the newspaper argued.

"Common sense and a longing for stability would dictate a modest vote of confidence for Mr. Reagan," the Guardian said. But, the newspaper added, citing American polls, the verdict appears to be that Reagan is "a pleasant fellow but a lousy chief of state."

Reaganomics is especially controversial in a country that, since 1979, has had Thatchernomics, a similar approach. Michael Foot, leader of the opposition Labor Party, has coupled the two policies in recent denunciations as a "threat to us all . . . fundamentally unsound economic policies being ruthlessly applied."

Those who argue that Reagan has discredited himself and therefore deserves to be, in the Guardian's phrase, "a lame old duck" acknowledge that having the Democrats in control of Congress would lead to a period of, at best, stalemate. The critics also concede that uncertainty in American policies have a substantial ripple effect on the rest of the world.

For example, it is understood that Reagan's Middle East initiative, which has won widespread praise here, would have a substantially reduced impact if the president were perceived as a declining figure. A weak president, moreover, would not be in a position to press any arms agreement with the Soviets that might emerge from talks in Geneva.

The first deployment of medium-range missiles in Europe is scheduled for the end of 1983, and paralysis in the Geneva talks would eliminate any hopes that those deployments might become unnecessary. Relations with the Soviets would plainly not improve if the United States were in a period of prolonged political transition (as the Soviet Union, in many respects, already is).

Even in the economic arena, a severe Reagan setback is not considered likely to shorten the international recession. Confusion in Washington would reduce business confidence and reopen arguments about how quickly to abandon monetarism and move toward reflation, analysts say.

Thatcher's aides said that her midterm crucible came in 1981 when her poll standing was low, inflation and interest rates were high and unemployment was rising. Using the GOP motto, Thatcher "stayed the course," they said, and today, while the economic situation in Britain remains serious, she is well ahead of her oppponents in every survey.

Inflation is dropping fast and interest rates are down. Thatcher is looking forward to a second term -- and wishes Reagan the same.