Truro, Cornwall, England — Seven hours after leaving London, the 23.59 overnight train from Paddington Station is well down into Cornwall. Early morning light gleams from a gray-blue Atlantic Ocean as the steward brings tea and we pull away from St. Austell station en route to Truro, Redruth, and Penzance.
The West Country, they call it, the spit of land at England's foot, where hundreds of thousands of summer visitors jam the tiny roads every year and the spectacular bays and cliffs are hung with memories of pirates and smugglers.
Today we have come to see a winter tourist. We leave the train at Redruth, and catch up with her as she bends over a counter and watches a Christmas cake being iced.
Only the day before, her firm, familiar voice was warning new Soviet leader Yuri Andropov that he needed to show firm evidence of arms reductions. This morning, it is deep in a knowledgeable assessment of icing.
''If you get it runny, you've had it,'' says the prime minister of Britain, smart in a pale-green woolen suit, concentrating wholly on the bowl of icing before her in a spotless workshop.
''Margarine is so much easier to cream. . . . I never could get used to a mixer. I always do mine by hand. . . . No, alas, I don't make my own Christmas cakes any more, but I do ice them.''
Margaret Hilda Thatcher is beginning a day very different from her usual round in Westminster and world capitals. She is at the Cornish grass roots, paying one of a series of monthly visits to local communities.
And she does so at a critical moment in British history, when her own style of unflinching self-confidence is under scrutiny as never before at home and abroad.
In Europe over the past three years, leaders in France, West Germany, Scandinavia, Spain, and elsewhere have toppled as voters look for strong action against inflation and unemployment. Yet the grocer's daughter from Lincolnshire is riding high.
She dominates the political scene at home, with an astonishing 41 percent support rating in the latest public opinion poll - and the changes abroad now make her the longest-serving leader of any major industrial democracy.
The Western world is awash with tragic unemployment - 11 million in Western Europe alone, 3.4 million here. History argues that any prime minister should be in deep trouble. Yet she actually gained popularity in November, according to the Marplan poll.
Partly, voters see Labour Party leader Michael Foot as ineffective. Partly, too, 70 percent of voters say other countries have unemployment as well. Voters show a fatalistic mood. Unemployment, they say, will go on for at least five years, and no party has all the answers.
To the despair of opposition parties, the issue is simply not a political liability for Mrs. Thatcher at the moment.
Few are neutral about this fair-haired woman in the green suit. The prosperous south hails her. The out-of-work north of England, along with Scotland and Wales, heartily dislike her.
The day in Cornwall is to make clear two things. One is that the ''Falklands factor'' is still important, not just because this corner of Britain, with its naval traditions, admires the victory, but because she herself is so buoyed by it. With an intense certitude, she invokes ''the spirit of the Falklands'' as the way to solve economic problems as well.
The other is that in person, she displays a sense of personal warmth that the television cameras do not pick up. In private, as well as public, she still tends to lecture rather than to talk, but she has a softer, more feminine side as well.
''I see you are well ahead with your Christmas cards,'' she observes at a table in Redruth. ''I haven't started mine yet.''
At a Coastguard rescue coordinating station overlooking the Atlantic Ocean at Falmouth, she stops at a collection box for the Royal Lifeboat Institute and fishes in her bag for a donation. Giving up, she has to borrow from her tall, self-possessed ex-company director husband, Dennis.
''I keep changing bags,'' she smiles. ''I'll pay you back.'' He pretends to be resigned. ''Don't bother,'' he says. Everyone laughs.
In the southwesternmost corner of Britain, Cornwall has little industry apart from its tin mines. Summer employment is high because of the tourists, and falls away in the winter, but the fall is steeper now. The jobless rate runs between 18 and 22 percent in the cities of Penzance and Truro, of Camborne and Newquay.
This is Conservative country. All but one member of Parliament are Conservative. The Cornish County Council is the only one in the country to have a majority of independent members, but ''they lean to the right,'' as local councillors say.
Liberals come second and Labour trails.
Mrs. Thatcher is surrounded by friends today. The only jarring notes are three eggs thrown by a young man outside a pottery in Truro (one hits a press camera and one a child, a young man is hustled away by police) and a question put by an elderly, well-dressed man. The man shouts ''How many thousands have you put out of work today?'' as Mrs. Thatcher arrives at a party gathering in the town of Bodmin. (A policeman tells the questionner to ''shut up.'')
''She's very, very popular,'' says a tall, mustachioed man at a party workers' lunch in Falmouth, a retired policeman who now runs an electrical repair shop.
''Almost every Cornish village had someone down in the Falklands, or knows someone who was there,'' he goes on. ''The speed with which we mobilized, and the result . . . well, people think she's marvelous. . . . Because she is.''
The Marplan poll shows her 41 percent rating eclipsing not only Mr. Foot but the Liberals' David Steel (17 percent) and the Social Democrats' Roy Jenkins (10 ).
Mrs. Thatcher and her husband ride in a black government Jaguar driven down from 10 Downing St. for the day. I spot one security agent and assume there might be one or two more. It is all very different from an American president on the move.
Five demonstrators politely ask a policeman where they can stand outside the building in Redruth. ''We just wanted to know,'' says one. His brand-new sign reads, ''Fall-out with Thatcher,'' and carries a nuclear disarmament symbol.
In Truro, Dennis Hills bounds forward to welcome her to a 200-year-old pottery that he has bought and restored. Mr. Hills is the type of man who simply refuses to acknowledge the economic recession. He is too busy.
For decades he made electrodes in a factory in Middlesex and took his annual holidays in Cornwall. Upon retiring, he saw that the Truro pottery was about to be replaced by an office block. He bought it. So far he has sunk more than (STR) 100,000 ($162,000) into it, creating a museum and employing 10 potters and 20 sub-suppliers.
''You have to have a team, and you have to work,'' he says to the prime minister.
''Indeed,'' says Mrs. Thatcher. Herself raised above a grocer's shop, she goes on: ''We stayed open until 7 p.m. on Thursdays, until 8 on Fridays and until 9 on Saturdays. You must believe in what you are doing.''
A few minutes later, calm and unhurried, she is talking to this correspondent and two others. ''We try to get out like this once a month,'' she says. ''We do something in the social field, and we support local business that creates jobs, like this pottery, and we think that the party workers, the people who stick with you through thick and thin, deserve an appearance.''
Did she think the so-called ''Falklands factor'' would last for long? She did not answer directly, but sounded her persistent theme once again:
''That was when Britain realized that it can still do the things for which she is famous. She can still defend liberty and freedom . . . and we can do it on other fields as well.''
Mrs. Thatcher stressed this point again and again during the day - to party workers at a cold chicken lunch at one spot, then at a church hall tea. Britain was once a generous builder of empire, she says. Now it has shown it still defends liberty and the rule of law. To the delighted awe of her audience, she says that the whole Western world now looks to Britain for judgment. Britain defends freedom and justice, qualities which are ''the essence of being British.''
Brenda Barrie, the wife of a local Anglican clergyman, nods. ''It's her faith in herself, and in the man in the street,that I admire,'' she says.