The women who worry Mrs. Thatcher

It is a most unlikely spot from which to challenge Ronald Reagan, Margaret Thatcher, and other NATO leaders: A sea of sticky mud surrounded by low brush, a log fire heating a blackened kettle, food piled on a table in the open air, lines of black trash cans, litter everywhere, a pile of sleeping bags beneath plastic sheets hung from overhead ropes.

Around the fire huddle a dozen or so women, trying to keep out a late afternoon wind with layers of sweaters, coats, gloves, jeans, socks, and thick boots.

Yet this is the scene at the main entrance to a United States Air Force base five miles from the city of Newburyin green Berkshire farmland - and it is one of the more urgent reasons why President Reagan is sending Vice-President George Bush around European capitals at the end of January to defend NATO nuclear policies.

British government officials say openly that the popular feeling represented by the women, and by other peace groups, is one of the main challenges Prime Minister Thatcher must meet in 1983, a year in which she will probably hold a general election, and in which NATO plans to install 572 cruise and Pershing missiles in Europe.

The name of the base - Greenham Common - has come to symbolize the growing antinuclear, anti-cruise, anti-Pershing movement across Europe, a movement that ranges from the Greens party in West Germany to the Dutch Reformed Church group, IKV, to the Campaign for Nuclear Disarmament (CND) in Britain.

Women around the campfire say they receive 200 letters a week from around Europe, some containing money. Visitors turn up regularly from around Britain. One of the grimy, muddy, defiant campers is a Japanese woman with her small child. Another is a German mother with twin five-year-olds who sleep in the back of a van and who go to school each day by taxi.

The women at the base, and other peace groups, plan to greet the vice-president with demonstrations. CND, which claims a membership of 250,000, is waiting for an answer to a letter to Mr. Bush asking him to meet its officials while he is in Britain Feb. 9.

Trying to warm herself by the fire, former arts student from Wolverhampton Bee Burgess, says, ''I think the Bush visit is a compliment to what we have achieved. We'll do something to mark his visit, don't worry about that.''

Back in north London, a national organizer for CND, Britain's fastest growing peace group, echoes her.

''Yes,'' says bearded Cambridge University graduate Dave Wainright, ''we'll have some kind of show of public strength so that Mr. Bush can see the strength of our convictions. We're working on the details.''

One floor below Mr. Wainright in a three-story dilapidated house in Finsbury Park that serves as CND national headquarters, general secretary Bruce Kent spells out what he would ask Mr. Bush if the vice-president agreed to see him:

''Why did the US vote against the nuclear freeze resolution in the (United Nations) General Assembly? Who opposes the formation of a nuclear working group in Geneva? Why not actively support the World Disarmament Campaign? Why not believe George Kennan when he says the nuclear arms race is out of control?''

Asked if he would have advice for the Soviet Union as well, Monsignor Kent (he is a Roman Catholic priest whose full-time CND duties are sanctioned by his local bishop) says, ''Yes indeed. Why do the Russians go on about a 'balance' of forces as if it was a relevant argument? Both sides have more than enough nuclear weapons to deter the other. It's time to cut down. . . .''

CND says it had 5,000 largely inactive members before NATO decided in December 1979 to deploy 572 cruise and Pershing II intermediate-range nuclear missiles in Europe to counter Soviet SS-20s. NATO also decided to negotiate with Moscow to try to remove the need for the missiles on either side.

Today, CND organizers say, the group has 50,000 fully-paid-up national members, a quarter of a million local members, an annual income of around (STR) 400,000 ($640,000) and applications for membership coming in at the rate of about 500 per week.

The Greenham Common base remains the focus of the debate, which in turn has helped cause Mr. Reagan to devote more attention to the protest movement in Europe.

Meanwhile Mrs. Thatcher has ordered her Cabinet to speak out more strongly against the antinuclear movement. She has appointed a new defense secretary, Michael Heseltine, with the specific task of regaining the public initiative.