WE CAN work it out. These most famous of all Famous Last Words are, of course, also the great words of conciliation, negitiation, and one is glad to hear the new British ambassador utter them.

When he arrived in Washington last month Anglo-American harmony was more than usually jangled by arguments over the Siberian gas pipeline, and you could hear gossip in London that if Sir Oliver Wright, the new ambassador, could not make some sort of progress restoring good feelings, he would possibly quit within a month.

In an interview recently Sir Oliver said he was hopeful. He sees signs, as it were. If you ask him if he feels better about the American stance than he felt in August, say, he says, "I will feel better about the pipeline when the sanctions are lifted."

After all, he goes on, "this thing is hurting the alliance more than it's hurting the Russians."

It's hurting, of course, because in an effort to thwart Soviet wealth from the pipeline, the American government has imposed sanctions against British and European firms supplying the Russians with manufactured items using American patents.

But then, "I am pretty confident we shall get the pipeline settled, too."

Besides, as he has said in his more poetic moments, the sea is often churned here and there on the surface, but 20 feet down the water is calm, and the ambassador does not underestimate the familial bonds and common interests that hold Washington and London together. Twenty feet under and we're OK.

And look at steel, he says. See what progress has been made on steel. He relies on any nation ultimately to choose a common interest above a sectional one.

In any case there are no signs of the new ambassador moving out of the handsome stone embassy on Massachusetts Avenue, quite the contrary. He has a photograph of his wife, Lillian, in his big office. Beside her is a fine brown-type dog that could conceivably be a Corgy ("Isn't, though. The runt of a mongrel litter; we had him 17 years") and men do not keep pictures of their wives and dogs in the office unless they feel settled.

One of his sons, Christopher, is in the real estate business in California ("and because he is in California he is known as Chris, but I call him Christopher") and there are three grandchildren. Sir Oliver and Lady Wright love to visit them. The English sometimes call him ambassador to California.

Someone suggested they are all nuts out there, but the ambassador said what a thing to say; if one said it about the home of the queen of England, one would be guilty of lese majesty. Though, as someone said, the American president is not royalty, you know.

"California has certainly contributed its full share" to the American glory, he continued, mentioning great names in science, etc., though he does suppose that "too much sun is bad for the brain"; indeed, one has but to look at their murky sky to comprehend British excellence in the world of intellect.

It may as well be known he sometimes wears red socks. He is given to shirts that suggest a reverie of Naples and the brim and blushful south. The one he had on was white striped deep blue bordered on each side with scarlet. His cuffs were not frayed. The British press has said he has frayed cuffs. What do they know?

There is deep public longing, apparently, for British ambassadors with windblown hair and frayed shirts. Sir Oliver said that like any other sensible steady man he does have old shirts and maybe some of them bear scars of battle.

Sir Oliver is 61, attended school in Warwick and the university at Christ's College, Cambridge. He had a distinguished career in the Foreign Service, ending (as he and everyone else thought) with his ambassadorship to Bonn.

When he retired as a diplomat, he was elected master of Christ's, in one of those academically vigorous contests in which some fellows wanted a man of academic distinction and not Sir Oliver. He does not hold it against any fellow who voted against him. He could see why some didn't want a lousy, smarmy diplomat (as he puts it). But Sir Oliver won, and was named master last May 11. On June 4, he gave up the post to accept the ambassadorship to Washington.

Ambassadors representing Britain are usually chosen from among diplomats who have worked their way up in the Foreign Service. They are rarely political appointments, as with us. If a British ambassador retires, however, he does not automatically become anything except (usually) a gardener, dog-lover and upholder of civilization generally. Sir Oliver's posting here was a special appointment of the prime minister, with the obvious implication that Sir Oliver is too valuable to be allowed to retire yet.

"The thing that astounds me is how understanding they have been," he said.

"After all, they went to a lot of trouble to elect me, and I suppose three weeks is a record for brevity. They didn't have to be all that understanding, did they. They made me an honorary fellow and I asked what duties were involved and they said absolutely none. And yet I can dine there in hall whenever I like, and have lodgings for 15 days a year.

"I was delighted, and promptly returned the honor to the 55 fellows of Christ's, with the same duties--none--and the same privileges here at the embassy."

Fifty-five fellows entitled to 15 days each.

Lady Wright is understood to be looking forward to scholarly guests.

The Wrights love the theater. They attended "On the Razzle" at Arena Stage this week, a recital at the Opera House and they think the tone of the capital is splendid.

"When I was young I was a bad actor," he said. Reminded that in America this suggests such improprieties as second-story work, he amplified. "I mean on the stage I was one who did not act well, though I loved it. I had the sense to give it up. But my wife is a good actress. We have not acted together for 20 years, but she has played in 'Blythe Spirit' and, oh, she played Lady Bracknell in 'The Importance of Being Earnest.' We have the Archway Theatre in our village Horley in Surrey.

"There are moments on stage," and here he leaned back a little, allowing the morning sun to look at his shirt and give up, "in which you know the spark from Heaven has fallen. You and the audience are together," and it is probably as heady a joy as mortals know.

Since the ambassador has been in Washington so briefly, not many people have met him, but one who did is a woman student at the University of Virginia who ran into Sir Oliver at a posh cocktail party for the Viscount Moore. Since the ambassador was going on to a dinner, he was in evening clothes and the girl assumed he was a waiter and asked him to fetch her a glass or organge juice. "Lovely smile," she reported, "but he never got the orange juice. It's one of those little mistakes you make in Washington."

He reads a good bit, with a "penchant for biography," though not eschewing novels. He thinks the world of "A La Recherche," and Jane Austen and wonders vaguely why the visitor has not read Trollope. He has not discovered marvelous novelists the world never heard of. Proust and Austen have already been discovered. So, for that matter, have Gaskell and Goldsmith.

"But I don't read best sellers. I am a great believer in the winnowing of time. As a result, I am a good 10 years behind what everybody else is reading."

A slight subtle vacuum suggested a little more recherching and prejudice, Austen-style, would do more for the world than most things on fall lists.

An aide bopped in to warn of time's wings out the window and the ambassador (on the theory that they will be always with us) did not leap at all but began discussing Owen Wister's book about the West.

"When you think of those hardships and how recent they were -- everything is named Death Valley --

"I was at a museum in San Diego looking at an old wooden road, made of railroad ties, and the date was 1906. Even as late as that, for wooden roads. My mother is old enough to have ridden on such a road. And then to catch a plane back to New York, five hours to the East Coast, when only a few years ago a man hoped he could make the journey before winter set in.

"For two and a half hours you fly over nothing. . . " and he let it sink in, the great bare mountains and the desert.

Some would say you fly four and a half hours over nothing. "Nothing" is relative and subjective, as so much in life is. The ambassador spoke of how easily we forget the hardness of life until quite recently even in the civilized world.

He paused and then said he's heard it said that all work is the same. Whether it's Pepsi-Cola or fixing fenders or diplomacy or anything else, there are obstacles, and pleasure in getting over them. Of course in any job you take the rough with the smooth, he went on, and then, possibly fearing that is too widely known, said "and sometimes the smooth with the smooth."

Maybe he meant tennis.

"I know a certain amount of work in Washington is accomplished on the tennis courts. I think well of tennis, but I am happy to say I have tennis elbow and do not play. I got my elbow from laying a brick path in the garden.

"I like to think I can lay out a garden as well as the next fellow, but the thing I really like is digging. The thing I hate is raking leaves."

It had not occurred to him, he said, to leave the leaves alone and call them a scientific mulch. Surely most diplomats know that, but Sir Oliver has a reputation for sincerity and straight shooting.

"I love the digging. The way the worms come up."