Before entering 10 Downing Street for the first time as prime minister late Friday afternoon, Margaret Thatcher determinedly ignored the shouted questions of reporters to deliver from memory a carefully worded plea for the British people to unite behind her efforts to change the direction of the country.

Then, just as she turned to go inside, one question catching her ear elicited a typically revealing, spontaneous response.

With whom did she want to share this historic moment, she was asked, perhaps the suffragettes who first won a place for women in British politics?

"Well, of course, I just owe almost everything to my own father, I really do," Thatcher stopped to explain with her now familiar intent earnestness. "He brought me up to believe all the things that I believe, and they're just the values on which I've fought this election. And it's passionately interesting for me that the things which I learned in a small town, in a very modest home, are just the things that I believe have won the election."

Those values - the worth of hard work, the importance of thrift, the opportunity for self-improvement, honesty and a deep religious belief in right and wrong - are the heart and soul of Thatcher's conservative philosophy. It is a simple, personal fundamentalist conservatism rather than the doctrinal ideology of the intellectuals and politicians of the right who have been her strongest supporters on the road to Downing Street.

She has a strong, unswerving belief in the rightness of her course. This is what gave her the courage to successfully challenge former prime minister Edward Heath for the leadership of a dispirited Conservative Party four years ago and then mount a crusade against socialism that won last week's election despite the voter's lack of affection for Thatcher herself.

Less noticed, however, is the way Thatcher has wedded her outspoken philosophy with a recently learned appreciation for practical, even cautious politics that belies her won frequently asserted belief that she is not a "pragmatic" or "consensus" politician.

Nothing ullustrates that fact better than her first important act as prime minister - her selection of a Cabinet representative of the entire Conservative Party rather than just the right wing most loyal to her.

Two of the top four positions went to men closely identified with the Heath government of the early 1970s that Thatcher repeatedly had repudiated: William Whitelaw, who becomes Thatcher's home secretary and deputy, and Lord Peter Carrington, foreign secretary. Both are considerably more pragmatic than true-blue Conservative.

Two others Thatcher appointed to key Cabinet positions - Employment Secretary James Prior, who will be dealing with Britian's powerful unions, and Agriculture Secretary Peter Walker, who will be dealing with the European Economic Community - are even more distant from Thatcher and her closest advisers in outlook and style.

For example, Thatcher was unable to hide her impatience at campaign press conferences with Prior's rambling explanations of his nice-guy sales talks to union leaders about the Conservatives' plans to restrict union power. Thatcher's most right-wing supporters warned that Prior was much too soft on the unions. Yet, she has given him free rein to try his go-slow approach of patient consultations with the unions and possibly avoid the king of ugly confrontation that brought about the Heath government's defeat in 1974.

It was Whitelaw and another non-ideological political technician, Humphrey Atkins, who has been the Conservatives' chief whip in Parliament for the past six years, whom Thatcher called first to Downing street Friday night to begin her government and finish planning her Cabinet.

Atkins was given the sensitive Cabinet job of Northern Ireland secretary, a choice welcomed by both Protestant and Catholic political leaders in Ulster because of his even-handed approach.

The tantalizing question for Britian - and for other Western democracies from Scandinavia to the United States where politics have been moving to the right - is just how far and how successfully Thatcher will pull Britain away from the welfare state democratic socialism it pioneered after the second world war.

"Just as the British Labor Party in 1945 was watched throughout the Western world as the first fullblooded practitioner of democratic socialism," political editor Simon Jenkins wrote in The Economist shortly before the election here, "so Mrs. Thatcher is confidently expected to become the first Tory prime minister to succeed in turning back that process begun in 1945. As such, she has aroused more intellectual curiosity than any British party leader in recent history."

To understand Thatcher, it is necessary to look as she suggests, at her upbringing in an industrious Methodist family in the then-thriving English Midlands market town of Grantham.Her father, Alfred Roberts, who left school at 13 to work in a grocery store, had moved to Grantham to manage a store.

He and Thatcher's mother, who learned to make and sell dresses from their home, saved to buy a small corner grocery, above which Margaret Roberts was born and raised with her older sister. Eventually, her father became a Rotarian, a part-time magistrate and a town council member, in addition to being an active lay preacher.

Years later, she rememebred how no play was allowed on Sundays, how "we didn't often go out to have fun together," how "we were taught what was right and wrong in very considerable details," and how her father "constantly drummed into me, from a very early age, 'You make up your own mind. You do not do something or want to do something because your friends are doing it.'"

Margaret Thatcher remains today a very serious woman with few pasttimes and a strong mind of her own.

Her father, who had always wanted to be a schoolteacher, also supervised his bright, studious daughter's education, encouraging a heavy diet of serious reading, taking her to lectures and involving her in political discussions at the local committee rooms and with council members who came into the store.

She was a hard-working, honor-winning, if not intellectually imaginative student in public school and Oxford University, which she paid for - in the days before the government provided a free college education - with a scholarship, money from her parents and her own savings.

While getting a degree in chemistry she became active in the Oxford Conservative Association and represented it at party conferences, where she attracted the attention of politicians looking for bright young candidates to train for Parliament.

She ran for Parliament in 1950 and 1951 in a safe Labor Party district. Although she lost, she increased the Conservative vote in the district, which finally elected a Conservative member to Parliament last week as Thatcher became prime minister.

While campaigning, she met Denis Thatcher, a paint company owner, whom she later married. When he sold his firm to a large oil company, they became well off, which helped make it possible for her to become a lawyer while bearing and raising two childrens. Tax law experience earned a reputation for diligence and reliability in budget debates after being elected to Parliament from north London in 1959.

She was a hard backroom worker in Parliament who served as education secretary in Heath's Conservative government. She made tactical mistakes in the heavy-handed way she made budget cuts ordered by the treasury and fought against the demise of elite public schools for bright children like the one in Grantham that prepared her for Oxford.

The publicity and bureaucratic scrapes she suffered overshadowed the fact that she increased education spending significantly overall and protected from the treasury budget cutters a rather radical innovation, the open university, which she saw as a vehicle for mass self-improvement.

She never doubted the principles underlying her actions as education secretary, but vowed not to repeat her errors of execution. She also believed with others in the right wing of the Conservative Party that the Heath administration had mistakenly continued to follow the preceding Labor government too far down the democratic socialist road.

Their intellectual leader was Keith Joseph, who in 1974, while the Conservatives under Heath were losing two national elections in one year, set up the economically right wing Center for Policy Studies as the brain and conscience of this new movement within the party.

Joseph was an admitted convert to evangelical conservatism from the ranks of those who thought conservative policies could be carried out through growing governmental involvement in society. But for Thatcher , Joseph's new right-wing economics simply fit with her lifelong philosophy of individual freedom, enterprise and responsibility.

When it came time to challenge Heath for the leadership of the party, Joseph, the touted front runner, decided not to run after losing support over an unfortunate parliamentary speech in which he seemed to be suggesting that too many low-income families supported by the government produced children too rapidly.

Thatcher dared to challenge Heath instead and won. She further suprised many in the party by gradually rebuilding its morale, largely through the strength of her personality in face-to-face conversation with individual Conservative members of Parliament. They, like many people who have met her privately, came away impressed with a warmth, personal concern and ability to listen that often does not come through in her meetings, public debate and encounters with the press.

During the campaign Thatcher laboriously rewrote all her major speeches and further embellished them in delivery with extemporaneous dashes of her personal philosophy. As one labor union leader here has observed, "One ought to listen to what she says very carefully.

There should be little doubt, therefore, that she will now bend her considerable will to trying to make the changes that she has been advocating for years in unvarying language. But it also appears that she will move cautiously, as she did during most of her carefully run election campaign, to try to avoid wasting through haste her historic opportunity.

She may have explained her view of her mission best on the last day of the campaign, when she promised " a calm but resolute return to the politics and economics of the free world." CAPTION: Picture 1, Margaret Thatcher enters 10 Downing Street. UPI; Pictures 2 and 3, KEITH JOSEPH and WILLIAM WHITELAW . . . Thatcher mentor, new appointee reflect a blend of idealism and pragmatism