FOUR BRITISH WOMEN are here on one of the world's oldest missions -- the search for peace -- and they talk of nuclear war and disarmament with the same fervor that has always lent that cause a special urgency. They say they are frightened for their children, frightened of the mounting nuclear tensions and they don't understand why the escalating nuclear arms race can't be stopped. And so they come here to America, four British mothers who see their country becoming a battleground, at the same time that four other British mothers are journeying to Moscow. They believe the Russians, too, are afraid of war, and that they, too, want peace. If both sides would just stop the arms race, say the British mothers, and then disarm. It seems so simple. And so naive.

Shenagh Gleisner of Manchester and Pat Dale of Leeds are two of the women who came here. They say their mission was conceived in the minds of two former teachers who now live in a Quaker home for the elderly in England. The two women put up f2,000 (about $4,200) in seed money to finance the trip. Gleisner is married to a doctor and has five children. Dale is married to a professional worker for the Society of Friends and is the mother of three. They are trying their best to be ordinary.

"Disarmament gets its strength from the Left," says Gleisner. "We're evidence of people who were not active before getting involved." The political mainstreaming of peace is not helped, however, by the fact that their base of operations here is the headquarters of Women Strike for Peace, which is hardly the political arm of the League of Women Voters.

Gleisner says that "a lot of things" they have to say are a "real surprise to Americans." Like what? "The facts are not too well known here," says Dale. "Most seem to feel that Russia has an edge in the arms race. They don't." They trot out conclusions from a left-wing European think tank and treat it as gospel. They talk with great confidence about cruise missiles and first-strike capabilities and NATO commitments to use nuclear weapons. And they talk with equally great confidence about the Soviet Union, which to hear them tell it, is practically bursting with peaceniks.

They don't know how the four women who went to Moscow are doing, but Dale says they are being welcomed by the Soviet Peace Committee. She says that the Soviets presented a peace petition with 180 million signatures at a United Nations disarmament session in 1978. The Russian people, she says, are afraid of war. "They're ringed on all sides. . . . They feel encircled. They've been invaded before by Europe."

How do they square their image of the beleaguered, peace-loving Russians with the invasion of Afghanistan? Gleisner answers that. "The message we are giving the Russians is, do you realize when you threaten Poland you could put detente back years? The Russians need to know from the British and from the peace movement that they make our life doubly difficult by acts like that. We ask them not to look at Americans with suspicion and distrust. We ask the Russians to trust beyond patience just as we would ask the Americans to trust beyond patience."

"Gleisner says the peace movement in Britain has "taken off" and the government is now campaigning against it at the same time it is discounting it. There is an effort, she says, to "dub us all as Communists. It's nice that we're all rather straight women coming here."

Maybe. But in the political analysis at the Women Strike for Peace office the hope for peace hinges on the true believers' assurances that the Soviet Union desires peace and fears war. "They are terrified by the prospects of war," says Edith Villastrigo, who got involved in the Women Strike for Peace effort in 1961 and who has gotten to a point where she tried to argue that the Soviet invasion of Afghanistan was in response to American activity in China. The Russians, she says, have women's peace committees that are supported by the government. Their government promotes the idea of detente, she says.

Women Strike for Peace and a collection of other liberal to left, old and new, groups are sponsoring a Mother's Day March for Nuclear Disarmament here Sunday. This will be the second peace demonstration in Washington in a week.

The British women say they are afraid of a nuclear war. There are Americans who are afraid and Americans who are concerned that we are hearing more and more about defense and less and less about peace. There is, as the British women found, a psychic numbness here. Who wants to think about what could happen?

The people who are paying attention are the old-line organizers and the kids, who were making housing arrangements for the people coming to town for Sunday's march, just as though we had never left the 1960s. It's an old and very limited response for the new nuclear anxiety and one that won't get a whole lot of support until they understand that peace will have a better chance when peace-loving people can march in Moscow, too.