ANYONE WHO has stood in Safeway lines, vacantly scanning People or The National Enquirer, anyone who was not deaf and blind during the last royal visit will hardly be stunned by the news that vast numbers of Americans are enthralled by the British royal family. We seem, rather strangely, to need them; they strike an important chord in our imagination. Politicians frenetically come and go, saying much, doing less. Film and rock stars are figures of our increasingly lurid fantasies. By contrast, the royal family (in spite of The National Enquirer's best efforts) presents an image of unbought grace, of serenity and undemanding distant elegance, of a lack of striving which nicely counterpoints the louder strains in American culture. And they are familiar; we have known them forever.

In this troupe, the queen mother is the established favorite, the member of the royal family best able to communicate genuine warmth and good will. Penelope Mortimer in her Queen Elizabeth: Portrait of the Queen Mother, acknowledges this and also, surprisingly, describes the queen mum as "the greatest sex symbol the royal family has ever known."

Mortimer, a well-known English writer, has made her first foray into biography under difficult conditions. Her aim, as she defines it, has been to produce "a plausible human being." However, secrecy veils the royal lives, and she has had, as it were, to deduce the woman from the image. She has succeeded. The book is methodically researched, snappily written, and those with royal fever should take it immediately to their beds until the temperature abates.

Queen Elizabeth is not a flawless book, but the flaws are actually interesting, for they are intimately connected with the difficulties of the subject. There is the chronic problem of getting the truth. Mortimer toys with various rumors -- was Elizabeth really in love with David? Or with James Stuart, his equerry? -- and makes much, too much, of Elizabeth's "feud" with the Windsors. But Mortimer's greatest problem is that she wants to take the royal family both ways -- now to be waspish and dismissive, now admiring and sympathetic. This uncertainty derives from a more fundamental problem -- the extraordinarily limited character of the royal family's life. The limitation is necessary; in a constitutional monarchy, they must be cut off from any real power. Their work is that of functionaries -- cutting ribbons, opening hospitals and orphanages -- strenuous business, perhaps, but not strong intellectual fodder nor gripping reading.

Royalty's most basic job is simple survival; during the war their chief function was "to stay put and be bombed with everybody else, eating spam off gold plates." If they themselves often chafe under these constraints (the book describes a wonderfully typical quarrel between George VI and Churchill, both dying to go to D-day, fighting over the opportunity), so must their biographers. Such territory offers limited range for sensitive probing and portrayal. But within that range, Mortimer does extremely well.

If Queen Elizabeth seems often more a chronicle than a portrait, if the heroine disappears for chapters at a time, it is because most of Elizabeth's story is not her own. ''Nobody marries one person. Even an orphaned bridegroom or bride carries a huge lump of history which is dumped, sooner or later, in their spouse's lap. When Elizabeth Bowes Lyon accepted Albert, Duke of York she took on an entire species.'' Mortimer, too, must take on that species, record its mutations and transformations. The decline of the extended family of European royalty is a poignant theme here. Before the Great War, George V, Elizabeth's father-in-law, had relatives reigning in seven countries; after 1945, the royal species was virtually extinct.

FOR ELIZABETH, the crucial members of the species were not the extended family but the nuclear family: the father, mother, and four brothers, whose lives and temperaments impinged on one another abnormally in the hot little tent that is royalty. In the royal context, natural, normal events have extraordinary consequences: when George V died, when David (King Edward VIII) went off to marry the woman he loved, life did not simply go on; it changed course radically.

Mortimer's sensitive portrait of the relationship between the Windsor brothers poignantly contrasts the first and second sons. David, the eldest, handsome, charismatic, insouciant, "a star royal performer," was also a loner, a melancholy Pierrot. Bertie (later George VI) only a year younger, was diligent, driven, obsessed by his own failure, sickly, and afflicted by a terrible stammer and consequent shyness. The pattern repeated itself with the younger two brothers. David and the third child, George, were close and their mother's favorites. Bertie was close to no one and indeed wished only to be left alone with his beloved shooting. Until he met Elizabeth. All that flowed from that meeting is the core of the book.

To Mortimer, Elizabeth is preeminently a performer -- from childhood nursery plays, straight through to the final phase when, triumphing over widowhood, she went on tour, "playing" from New York to Nyasaland, enchanting all. Elizabeth's charm is seductive, flirtatious yet maternal, sensuous but impeccably upright. Indeed, Mortimer suggests that the energy of her performance derives from the sublimation of great sexual reserves. Her sexuality is not blatant. As Duchess of York, she presented the country a tableau of tranquil family fun which contrasted happily with the shenanigans of the Prince of Wales.

The performance was not always fun. Elizabeth accepted Bertie, then Duke of York, with reluctance. With him came a host of onerous royal tours and tasks. However, she "played the part like a trooper," bearing heirs, helping her husband cure his stammer, preparing for the unforeseen future. It paid off. After the shock of the abdication, they went on tour and returned to stardom. ''Bertie and Elizabeth, after flickering uncertainly for a time, exactly fitted the roles left empty by Douglas Fairbanks and Mary Pickford -- fallible and yet perfect, exalted in themselves . . . fluttering in tight corners, winning through . . . . 'George the Good' and his Cleopatra were, at that moment, an historical necessity.

"That moment" was 1939. Elizabeth was delighted; moreover, she was adaptable and her repertoire versatile. In wartime she "changed her image from fairy queen to a sort of exalted Mrs. Miniver," dowdy, comfortable, resolute, inspecting bomb craters and old people's homes, nearly always "amused and sympathetic." With her daughter's accession, she took on her final role -- the queen mother. "All she has to do when she drops from a cloud, fresh as a daisy, is to generate love, delight, and enthusiasm." There is more here, Mortimer suggests, than just an act. Fifty-six million Britons have not misplaced their loyalty: beneath the delightful exterior really is a nice woman.