American 'independence' in England; Back Home, by Michelle Magorian. New York: Harper & Row. 375 pp. $14.50. Ages 12 and up.

Young adults want very much to be accepted by their peers, as well as by their parents and teachers. In her second book, Michelle Magorian has captured the frustration and anger of a young girl unable to gain acceptance by either her schoolmates, her teachers, or her very proper English mother and grandmother. Ms. Magorian, who is English, also deals with the strong anti-American sentiments vented toward this girl at home and at school.

When 12-year-old Rusty Dickinson returns to her own family in postwar England after spending five years in America, she hardly recognizes her mother. Her mother doesn't seem very pleased to see her and insists on calling her Virginia instead of the nickname she was given in the United States. Not only that, her mother, who is an accomplished mechanic for the Women's Voluntary Service, is always rushing off to fix a car that has broken down rather than spending time with Rusty.

Ms. Magorian deftly handles Rusty's problems in adjusting to life in England. Sensitive to the differences in language and life styles between American and English youth, the author realizes how subtle these differences can be and the great difference these subtleties can make.

Upon her return from America, Rusty finds the demands of a British life style stifling and rigid. She doesn't like the tea; she's not used to the dry bread, sugarless cakes, or margarine instead of butter; the houses look grimy and dirty; and the clothes everyone wears are faded and patched. To make matters worse, Rusty is constantly being told to ''be polite,'' ''act like a lady,'' and ''don't be disobedient.'' With her American family, the children and the parents all spoke their minds and openly discussed problems. In England, as Rusty soon finds out, children are to be seen and not heard.

So when Rusty's mother tells her that she will be attending boarding school, Rusty is elated. She has visions of secret passages, midnight feasts, and cozy chats with friends after lights-out.

Instead, Rusty's schoolmates refuse give her directions to classes because she talks with an accent. They cruelly comment on her accent, sneer at the ''traffic light'' colors she wears, and are shocked that she has a photo of her American ''brother'' on her bureau. She is also severely reprimanded for talking with a boy.

In the following passage, Mogorian skillfully depicts the antagonism Rusty faces in England:

When the mistress had finished writing out six verses, she began walking around the desks looking over the girls' shoulders as they hurriedly went on writing. When she reached Rusty's desk, Rusty looked up at her.

''Those are pretty lines, aren't they?'' she said.

From one lonely cloud

The moon rains out her beams, and heaven is overflowed.

''Did I ask you to speak?'' Miss Webster snapped.

''No, ma'am,'' said Rusty, startled.

''No, Miss Webster,'' the teacher corrected. She picked up Rusty's jotter, took one look at it, and flung it down on the desk. ''And this writing will not do. Didn't you learn anything at your American school?''

''Not if her maths and French are anything to go by,'' muttered one of the girls.

After several weeks at boarding school, Rusty decides to sneak out at night and explore the countryside surrounding the school. She and a young boy named Lance, who was also evacuated to America during the war, find a ruined bomb shelter that they call their ''cabin in the woods.'' It is their escape, a place where they can merge their American/English identities without being ridiculed by their peers.

When Rusty's father returns from Japan, her situation gets worse. Her mother has become considerably more independent during the war years. Rusty's younger brother Charlie, not used to his father's strictness, becomes very dependent on his mother; even Rusty cannot accept the harshness and coldness of her father.

It is her mother's new independence that helps Rusty recognize that her family has changed and that things can never be the way they were before the war.

The depth of this book makes it more than light reading, and Magorian's skillful writing makes a second reading rewarding.