The nations inflation rate dipped below doubled digits last month for the first time since summer, the Labor Department reported yesterday.

The consumer price index rose 0.7 percent in January after moving up 1 percent or more in each of the four preceding months. The January increase works out to a 9.1 percent annual inflation rate. Inflation ran at a 13.4 percent rate in December.

The department also reported consumer prices in the Washington area rose 1.4 percent in the two months ending in January. In all 1980, area prices rose 11.9 percent. The department said that a 1.7 percent increase in housing costs accounted for more than half the total December-January increase here.

The moderation in January's prices was reported as Federal Reserve Chairman Paul Volcker was telling Congress the public should not be lulled into think there will be quick, easy drop in inflation.

He said the government must keep fighting it, and, for his part, announced that the Fed was tightening its monetary growth targets half a percentage point. In the past, tighter monetary policy has generally produced higher interest rates and slower economic growth.

Murray Weidenbaum, chairman of the Council of Economic Advisers, immediately cautioned that the January report "provides little basis for optimism with regard to the underlying rate of inflation."

Specifically, Weidenbaum indicated concern over rising energy costs. "A slight decline in food prices was counterbalanced by a sharp rise in energy costs, particularly gasoline," he said. "Food is an especially volatile component of the price index and cannot be counted on to offset further likely increases in energy costs, as U.S. oil prices rise to market levels."

The January report did not reflect the sharp increases in home heating oil and gasoline prices that followed White House decontrol of oil prices late last Month. The White House action came just one day before the Bureau of Labor Statistics completed its January price survey.

"The survey probably didn't pick up any of that," a BLS spokesman said.Since decontrol, the major oil companies have raised gasoline and heating oil prices more than twice as much as the White House had expected. Department officials refused to predict decontrol's impact on February prices.

Gasoline prices nationally have risen approximately 10 cents a gallon since late January. This alone would raise the February consumer price index 0.5 percent.

As to interest rates, Henry Kaufman, the highly influential chief economist for Salomon Brothers, predicted another jump later this year. Although interest rates have begun to recede from this winter's record levels, Kaufman predicted they might set new records. The prime interest rate banks charge their preferred customers reached a record 21 1/2 percent late last year.

The Reagan administration has predicted a sharp and rapid decline in interest rates once the president's new economic program is enacted by Congress. Most economists outside the administration predict slower interest rate improvement.

In consumer prices, one of the biggest changes last month was a 0.4 percent drop in grocery store prices. It was the first monthly decline in grocery prices since early 1980. The sharpest food price declines were for meats, poultry, fish and eggs, which dropped 2.4 percent in January. Fresh fruit and vegetable prices also declined.

The food price decline was offset basically by increases in almost every other sector. During the months, housing costs rose 0.8 percent, transportation 2.2 percent and medical care 1.1 percent.

The cost of home fuels and utilities rose 2.1 percent in January, with the price of fuel oil rising 7.5 percent and electricity and natural gas 1 percent. p