Krippendorf’s Tribe : <i> by Frank Parkin (Atheneum: $13.95; 192 pp.) </i>

Eight or nine years ago, England had a prodigiously hot summer, marked by brilliant sunshine and whole weeks of blue skies. It started as a welcome novelty and ended up as something of a horror. Drought turned the emerald-green island into burnt-out amethyst. And it did more: It brought out an accumulating shabbiness and decay that had seemed less noticeable under the overcast.

In the different light, all the phrases about Britain’s becoming part of the Third World took on a different light. A whiff of the tropics was no joke; they turned out to be Levi-Strauss’ sad tropics.

I suspect that the memory of that summer is one of the things that underlies Frank Parkin’s rattly but extremely funny satire. If Eliot’s world ended not with a bang but a whimper, the England of “Krippendorf’s Tribe” is going under, not with a whimper but something between a snarl and a smirk.

Set no more than three or four years into the future--and more disconcerting for being so recognizable--British life is an unpalatable blend of leftover egalitarianism, right-wing nastiness, decrepit consumerism and outbursts of violence.

In the most matter-of-fact way, we hear of bread riots, pension riots, mortgage riots. Hanging has been revived and put on television. Union leaders face deportation. A school principal, wearing blue jeans and love beads, affably enumerates his more recent problems: stranglings in the boys’ bathroom, an outbreak of religious mania in the fourth form and a leprosy scare.

Affability is the key; none of this matters much. The joke and the wink that symbolized a stalwart people during the Battle of Britain are now the symbol of a banal spinelessness. The normal is as discouraging as the extreme. The supermarkets carry Portuguese caviar, Korean whiskey and wine in six-packs next to the shelves of banana-fudge frosting. The universities are crowding out academic subjects in favor of practical ones. One of the crowded-out results is James Krippendorf.

We first see him, tall, balding, apparently abstracted--and, as it will turn out, breathtakingly practical--when he is trying to get his three children off to school. His teen-age daughter, Shelley, wearing a dress that she has fashioned out of aluminum foil, has just hit Edmond with a wok for stealing her vibrator. Mickey is in trouble for singeing the neighbor’s cat with a homemade napalm device constructed out of kerosene and corn syrup.

James has a wife, Veronica, but she is a journalist who spends most of her time covering outbreaks in Libya or Haiti. When she does turn up, it is to make various peremptory demands. Krippendorf is in full charge of his household of hellcat children. Having lost his university job, he is writing a paper on the Shelmikedmus, an Amazonian tribe, for which he has received a hefty research grant.

However, he has already spent the grant on a new car and a vacation. Furthermore, the Shelmikedmus are imaginary. They are, and it is the book’s most ingenious conceit, a wacky image of his own surreal menage.

Among the Shelmikedmus, for example, domestic work is the principal source of self-esteem. Naturally, it is reserved for men. “In Shelmikedmu eyes,” Krippendorf writes, “the only fully rounded personality, the only truly complete human being, is one who sweeps in the morning, scrubs in the afternoon and cooks in the evening.” Women, he continues, are relegated to the despised task of hunting. Most accept the role, though there are occasional protests. Instances of spear-burning have been reported, he writes, “and now and then a young woman may be seen swishing her bow to and fro in pathetic imitation of a sweeping motion.”

The children are a steady source of inspiration; sometimes in reverse. Treated with terminal contempt at home, Krippendorf writes that the Shelmikedmu children have their mouths bound so they won’t speak. At night, they soothe their careworn father by rubbing him with alligator fat.

In a society that has lost its use for scholarly pursuits, no scholarly fraud goes unrewarded. “Exotica,” a soft-porn transfiguration of “The British Journal of Structural Anthropology,” offers Krippendorf handsome fees for doing a series of sensational articles on his tribe. Photographs are wanted as well, so Krippendorf colors his children with body paint and has them demonstrate circumcision rites with the household’s potted plants as a tropical backdrop. When sexier material is required, he seduces and photographs the Filipino mother of one of his children’s schoolmates.

Using an English family to derive a primitive Amazonian tribe is only part of Parkin’s satire. As the book goes on, the children’s primitivism turns tropical. By the end, they have killed and eaten their housekeeper--Krippendorf joins in, taking notes all the time--and have begun hunting the neighbors’ pets for fresh meat.

Parkin is a political scientist and sociologist--one of Mickey’s pranks is erasing the sociology course from his school’s computer--and “Krippendorf’s Tribe” is his first novel. It has its weaknesses. A number of the incidents seem superfluous. The momentum is erratic after a strong beginning; the children’s comical monstrosity gets more clamorous but not more interesting as the book goes along, and the ending is more cop-out than climax. Finally, the author pops his jokes too often and too lavishly. Mickey’s proposal to bury the housekeeper in the garden acquires whimsy but not humor when Krippendorf objects that he does not want his runner beans disturbed.

Still, Parkin has made his book something more than a comical contraption. His crooked anthropologist and the invented tribe swoop in at a flaring angle to the reality they satirize, and their passage more than makes up for a good deal of stumbling.