Sheepishly, the demonstrators dug into their pockets and coins dropped into the lifeboat.

"The workers will never be defeated," exclaimed one young woman as she made her contribution. The take from the socialists to the charity, said the aide, was five pounds, two pence, or just under $10. Thatcher, he added, kept her word and doubled it. The protesters scattered.

Margaret Thatcher is a no-nonsense person, as the Argentine junta found out in the Falklands. When she sets a course, she keeps to it. On a smaller scale, if she makes a trip to this corner of Dorset, about a hundred miles southwest of London, to aid the Royal National Lifeboat Institution, she makes certain that no ragtag demonstrators will get the best of her.

ABOUT ONCE a month, Thatcher's advisers organize trips like this one, forays into the British hinterlands that have all the predictable political purposes. She meets with local Conservative Party activists, business leaders, schoolchildren and, on Friday, the wives of British Marines, whose husbands served the Falklands cause.

The trips are not meant to be news-makers. Even after the South Atlantic triumph and her improved rating in public opinion polls, she has avoided grandstanding around the country.

But the journeys do afford a rare opportunity to see Thatcher up close, to watch her make conversation with officials, smile and nod, and generally to get a feel for how she operates outside the rough-and-tumble discourse of Parliament, the only place most reporters ever see her.

In the course of a day, you can get near enough to the prime minister to admire the scarabs on her bracelet, her blue suede pumps, her kidskin gloves--and close enough to her husband Denis to see his argyle socks. But you may not talk to her. Those are the rules.

So it was that in a full day of travel Friday Thatcher was never asked about the furor over the intruder found in the queen's bedroom, about Britain's national rail strike or the rumors that abounded in London of some new spy scandal about to break.

A reporter for a local radio station wanted to question Thatcher about a new computer program she had announced for schoolchildren at another stop on the schedule.

"That all?" the press officer asked skeptically.

"Promise," said the reporter.

THIS PROXIMITY without access is an almost complete reverse of the situation that tends to prevail on similar out-of-town trips by an American president. President Reagan hardly ever takes a public step outdoors without answering a query on the topic of the day. But wherever he is, a phalanx of security surrounds him and an entourage of dozens attends him.

By contrast, Thatcher travels light. She is escorted by a local police vehicle. Her car is not a limousine but a Daimler Sovereign 4.2. There are three security men, who leave plenty of room, a press aide, her parliamentary private secretary Ian Gow and, on this trip, husband Denis. Instead of a cavalcade of press buses, there were only a few journalists, mainly there to photograph the prime minister in some uncharacteristic moment, such as wearing protective glasses in a factory.

Would she ever be seen in a hard hat or other kind of unusual headgear, the press aide was asked? "Never," he replied.

Crowds were sparse also. Aside from the demonstrators in Poole, there were three women opposed to vivisection who tracked Thatcher much of the morning. Employes at the two factories she visited were lined up at the end, a few with plastic Union Jacks, and there was polite applause. There were no specially gathered spectators along the route.

In other words, there is almost none of the circus atmosphere of an American presidential journey and little of the tension that someone in the crowd might do something awful. For all the violence and occasional terrorism related to Northern Ireland, for all this week's focus on security lapses at Buckingham Palace, the British do not yet anticipate the worst that can happen to their leaders as Americans have learned to.

As for style, Thatcher on the hustings is not a warm figure. She exchanges a few words, usually confined to the subject at hand,with each person to whom she is introduced. At Flight Refueling Ltd., the company that makes equipment used by British planes flying long distance to the Falklands, she coolly warned the executive showing her around, "Everything you say can be overheard and will be."

Keeping tightly to the schedule is plainly important. Another executive at Flight Refueling, a distinguished looking man with a monocle and wearing a pin-stripe suit, followed the prime minister's progress with a timetable down to the minute. As she passed a final juncture, he consulted the paper and declared proudly, "Dead on time."

About the only place Thatcher might have unbent was with the Marine wives. But that was listed merely as a "private engagement" on her schedule, so no reporters would attempt to join her. With the schoolchildren, she watched attentively as they went through their computer paces, but there were no jokes or supportive quips.

Thatcher's husband, who is retired but serves on the board of several British companies, always walks a few paces behind his wife. He gets a separate person to brief him and, on the whole, seems more relaxed than the prime minister. At the school, one youth had programmed a toy tank to do elaborate maneuvers back and forth. Mr. Thatcher found the object irresistible and got down on all fours for a better look. That's when you could see his light blue argyle socks.