Greenham Common, England — ''I like to think of a sort of groundswell of public opinion'' against nuclear weapons, ventured Heath King. She was wearing a knitted cap against the freezing temperature as she demonstrated outside the base at which American cruise missiles have recently arrived. She was obviously enjoying the sisterhood of the ''demo,'' the shared commitment to the cause of peace, the on-the-hour noisemaking of whistles, drums , tambourines, saxophones, pots and pans, and vocal whoops, the occasional surge of songs of solidarity.
She and her grown daughter had come down by coach from Nottingham that morning. They were holding aloft a home-sewn banner with a vivid rainbow crossing a tree and a symbol of the Campaign for Nuclear Disarmament (CND). Their local chapter has been active for a year and a half, holding a peace festival in Nottingham and running a storefront information center.
Mrs. King recognized that not everyone shares her priorities. She understands why most voters cast their ballots on economic rather than nuclear issues last summer when Britons reelected the pro-missile Conservatives. But she sees a real public impact by the CND campaign and the two-year-old Greenham Common women's campout: ''It got the issue onto the front page and looks like (we're) keeping it there.''
She is disappointed that the protesters were not able to block the deployment , but she is prepared for a long haul. ''It took us 40 years to get here,'' she says, echoing words of CND General Secretary Bruce Kent, ''and it may take us another 40 to sort it out.''
Mrs. King's comments go to the heart of the matter. The long, slow struggle to convince the public that nuclear weapons are intolerable is the key task that nuclear pacifist movements like CND have set themselves.
In recent years they have succeeded beyond their fondest dreams. CND membership has soared in the 1980s, after staying at a low level for the previous two decades. Moreover, the membership has spread through the British countryside to towns and local communities that had barely heard of CND in its previous heyday in the 1950s and early 1960s.
There is a profusion of professional groups - doctors, lawyers, teachers, architects - embracing nuclear disarmament, or at least rejecting the American cruise missiles. Antinuclear demonstrations nowadays regularly attract hundreds of thousands of protesters. Public opinion polls consistently show that a majority of British voters oppose the cruise.
And yet, if you talk to the residents of Newbury, the town at the foot of the Greenham Common hill, you get a different story. They - like the townspeople of Schwabisch Gmund outside the first West German Pershing II base and (to a lesser extent) the villagers of Woensdrecht, the future Dutch cruise base - accept the new missiles as a fact of life. It's a presence they would prefer not to have in their own back yard, but it's nothing they're going to get excited about.
Nor, for the conservative English and German townsfolk, do the deployments warrant demonstrations that disrupt normal life.
''They (the demonstrators) break every law they can,'' agreed two Newbury women.
''They think there's one law for them, one law for the police,'' stated one of the women as her friend nodded. ''Newbury used to be a very quiet place before the police started flying by (in their helicopters).''
So which public is going to predominate now that stationing has finally begun - the one that's troubled by the new Euromissiles, or the one that resents the trespasses of the protesters? The former, according to the peace activists. The latter, according to the British and West German governments.
British Secretary of Defense Michael Heseltine, the man charged with the hard sell of the government's nuclear policy, has argued that once the new missiles are on the ground, they will no longer stimulate such intense controversy. And Bonn officials contend that the pitch of anxiety that has been a conscious feature of the West German protest simply will not be maintained after a few months have gone by and war hasn't broken out after all.
Antinuclear activists scoff at such dismissals and say that news of their demise has been greatly exaggerated. The protesters' morale sank after the British election last summer, they say, but it revived again in the fall - as the record turnout at the big Oct. 22 London peace rally showed. CND membership is currently continuing to grow by a net 3,000 a month, according to Christian CND organizer Barbara Eggleston and her staff.
Inevitably, both sides rely on opposition polls to prove their case. Inevitably, the evidence of the polls is contradictory.
When asked in the abstract if they want new missiles - or when given a choice only between deployment or arms-control negotiation - most northern Europeans reject the American missiles.
When asked if their countries should deploy new missiles if the Soviets don't reduce their SS-20s, however, most citizens (except in the Netherlands) accept the new missiles. And when asked to rank their worries, most northern Europeans list nuclear weapons and war well below unemployment - as the West German election in March and the British election in June showed.
Peace activists, especially in West Germany, therefore take the former results to demonstrate that they have the majority on their side in the missile debate.
Governments take the latter results to demonstrate the validity of their pro-missile policy.
And both sides, of course, accuse the other of rigging the questions in various polls to produce the desired results.
Any number of national and international opinion polls in the key countries of Britain and West Germany illustrate the dichotomy of public antipathy toward new missiles - but reluctant acceptance of them if the Soviets don't exhibit more arms restraint.
(Britain and West Germany are crucial because they are two of the three NATO countries that are beginning deployments now, and the third stationing country, Italy, has no strong antinuclear movement. The Netherlands is crucial because nuclear pacifism is strongest there and is regarded as a model by peace movements in neighboring countries).
An example of the ambivalence is provided in EMNID polls last September. Of West Germans 18 years and older, 58 percent favor Western deployment of ''modern nuclear weapons.'' But 61 to 66 percent of those 14 and over oppose de-ployment ''if the negotiations between the USA and the Soviet achieve no results.''
Even more instructive, perhaps - since policy battles are always fought out among the ''attentive public,'' not the indifferent masses - is an ''elite poll'' in Britain, West Germany, the Netherlands, France, and the US by the West Berlin International Institute for Comparative Social Research. A series of structured oral interviews in 1982 indicated that:
* A majority of the elite in each country favored new NATO deployments ''unless the USSR reduces . . . its SS-20s to mutually acceptable levels.
* No elite majority favored ''unilateral steps toward disarmament. But,
* Only a small minority would approve going beyond deterrence to the actual use of nuclear weapons in any war (as official NATO doctrine allows). On this question France was an exception, with 54 percent endorsing a possible nuclear response to any Soviet-bloc conventional attack ''in order to bring the war to an end quickly.'' Only 24 percent in the Netherlands and the US endorsed such a nuclear response, 17 percent in West Germany, and 15 percent in Britain.
These results suggest that the peace movements have gained many converts in the years since detente collapsed. But they also suggest that governments can carry out the scheduled deployments - if they move carefully.