THE SILENT TWINS By Marjorie Wallace. Illustrated. 230 pp. New York: Prentice Hall Press. $16.95.

WE assume we are all individuals, autonomous, unique - and this assumption is suddenly tested, even shattered, when we meet twins. It is not just the biological rarity and extraordinariness of identical twins that so impress the imagination. It is the exact, the uncanny, doubling of a human being, a doubling (we may see, or imagine, or fear) which may extend to the innermost, most secret depths of the soul. There is always a shock - of interest, surprise, pleasure . . . and consternation - on encountering twins. We gaze from one to the other: identical faces, expressions, voices, movements, mannerisms - and feel a mixed sense, a double sense, of both marvel and outrage (this is reflected in some cultures, which sometimes revere twins and sometimes destroy them).

The scientific study of twins is little more than a century old, and was inaugurated by Darwin's cousin, Francis Galton. Galton was the first to cast a Darwinian eye on the inheritance and heritability of man's highest functions. Through the study of twins - especially identical twins, early separated and separately reared - it would be possible, wrote Galton, ''to weigh in just scales the effects of Nature and Nurture, and to ascertain their relative shares in framing the disposition and intellectual ability of men.'' He concluded, with certain reservations, that Nature here showed itself far stronger than Nurture.

Galton perceived that the lives of twins seemed to lie under a sort of destiny or fatality, but this fatality, this necessity, he saw wholly as constitutional and inborn. It was reserved for a succeeding - dare we say Freudian? - generation to see that there was another fatality: the special twin relationship, interaction, ''situation'' (although this had long been recognized by novelists, especially those, like Thornton Wilder, who were themselves twins - thus the magnificent depiction of the identical twins Manuel and Esteban in ''The Bridge of San Luis Rey'').

The twin bond was minutely examined by Dorothy Burlingham, the lifelong colleague of Anna Freud. She opens her book ''Twins'' with a consideration of the common (but oddly overlooked) fantasy of having a twin, and its contrast to the actuality of having a twin: ''In the fantasy, the relationship to the twin is imagined as an untroubled and unchanging one. Observation of reality shows the twin relationship threatened by negative and aggressive feelings, which manifest themselves in competition, rivalry for the parents' love, jealousy, and the wish to dominate the other. . . . Yet the need for the twin makes each partner adapt and adjust to the personality of the other. In this manner the twin relationship becomes the closest known tie between two individuals.''

Usually, twins are able to differentiate fully, to become complete individuals while maintaining this singular tie. But sometimes this tie may become pathological - Miss Burlingham speaks here of the twin-pair becoming a ''twin-team'' or ''twin-gang,'' feeling, doing everything together, caught in a helpless entanglement or embrace. Such an embrace - at once yearned for and intolerable - tends to be both symbiotic and destructive.

In 1982 Marjorie Wallace, a writer for The Sunday Times of London (and author of a powerful and moving screenplay about a family who adopted a severely handicapped thalidomide child, ''On Giant's Shoulders'') found herself the reporter of a singular case -the trial of apparently mute, identical twins on charges of arson and theft. ''It was an extraordinary occasion. The twins, tiny and vulnerable, said not a word apart from a few grunts which the court interpreted as pleas of guilty. The unemotional legal pantomime went on around them without touching them.''

June and Jennifer Gibbons were sentenced to indefinite detention in Broadmoor, a notorious institution for the criminally insane. The shock of this sentence, combined with the strangeness and apparent helplessness of the twins, moved Ms. Wallace to investigate -to elicit the entire life histories of the twins, and, above all, to explore their extraordinary inner worlds. This investigation, with affinities to a case history, a psychoanalysis, a detective story and a novel, is unrolled in ''The Silent Twins.''

Such an investigation could never have reached the depths it did without the writings of the twins (there had been no intimation in court that they were anything more than ordinary delinquents). But Ms. Wallace, visiting their home, found ''a small room full of black plastic dustbin bags . . . an extraordinary collection of diaries, typed manuscripts of stories, novels and poems, illustrated strips and books of drawings.'' These writings of the twins to some extent form the core of this book.

The twins' birth, their parents, their early years, seemed unremarkable enough. Their father, an intelligent if remote West Indian, worked as a technician with the Royal Air Force; their mother is described as ''sensible and intuitive.'' They had three children before having the twins, June and Jennifer, in 1963. Though life appeared comfortable and easy enough on the surface, there must have been special problems and strain -their father, one of the very few black West Indians in the air force, continually moved his family from one posting to another. We are told very little, too little, of the earliest years of the twins, only that they were ''full of life and played happily together, deeply involved with one another, but they were late talking. By the time they were three years old they were only able to put together the simplest two- or three-word sentences and even the few words they knew were indistinct.'' But curiously, their parents were not particularly worried, and in every other way they seemed healthy and happy. WHEN they were 5 and in school, their teacher noted they were ''inseparable,'' and would not talk to her, though they talked to other children. But there was still, extraordinary though it sounds, no real anxiety, no sense of anything deeper amiss, in either the mother's or the teacher's mind. The twins were ''very shy'' -that was all there was to it. It was only by the time they were 8 1/2, and transferred to a new school, that the severity of the twins' problems, suddenly exacerbated, became undeniable. They found themselves laughed at in class and bullied and baited in the playground. They were forced to cling more tightly to each other, to strengthen the walls of their twinship. They stopped trying to communicate with outsiders and, even within the family, became more isolated, chatting away by the hour to each other and their dolls in an unintelligible secret language of their own.