A new privately computed index shows that the rate of inflation in four basic consumer "necessities" has been running at double-digit rates, far in excess of the over-all inflation index complied by the Government.

For the three months ending with April, this basic index rose at an annual rate of 12.6 per cent, compared with the Consumer Price Index advance of 9.5 per cent for the same period, according to the National Center for Economic Alternatives.

The four "necessities", making up almost 70 per cent of consumer spending by four-fifth of the population, are food, energy, medical care and housing.

The National Center for Economic Alternatives is a Washington-based economic research organization devoted to seeking new or non-traditional approaches to current problems.

Gar Alperovitz and Jeff Fauz, co-directors of the center, have argued in earlier reports that the Carter Administration should concentrate its anti-inflation effort on the four basic areas contributing most to inflationary pressures.

In the new report, they listed about 100 measures they said could be used to counter basic inflation, including an increase in beef imports. President Carter last week announced a 200-million-pound increase in voluntary beef quotas.

But the authors would go beyond the Carter action, amending the law to allow beef imports to rise automatically when domestic beef supplies fall or prices rise.

The report estimated that the recent annual inflation rates (end of January through April) have been 18.7 percent for food, 7.8 percent for energy, 8.4 percent for medical care, and 11 percent for housing. Non-necessities went up at an annual rate of only 3.9 percent.

Alperovitz and Fauz said that "contrary to widespread opinion, the primary source of inflation in the basic necessities have been factors other than wage increases." In housing, for example, they noted that construction labor costs have actually declined slightly from 1970 to 1977, but that land and monthly financing costs have jumped.

"Ironically," the report said, "the latter is significantly related to the Federal Reserve Board's strategy of raising interest rates in the hope that this might slow general inflation."

Over the past decade, they said, inflation in the prices of most goods and services the typical consumer buys have been pushed up by "extraordinary shocks" such as cold winters and oil price boosts, or energy-intensive costs of food. Then, in most areas, wages attempt to catch up with prices.

"Current inflation has little to do with excess demand, and therefore should not prevent efforts to achieve full employment," they said. "Neither balancing the budget nor restrictive monetary policy would significantly alter the level of inflation, since it derives from quite different factors."

The suggested list of ways to attack inflation in both the short run and long run was forwarded to the Council on Price and Wage Stability, the federal wage-price monitoring agency.