Consumer prices rose 0.3 percent in January, the smallest monthly increase since July, 1980, the government reported yesterday.

The increase, which the government said works out to an annual inflation rate of 3.5 percent, was hailed by the White House as "very good news indeed," marking "another forward step in the struggle against the worst economic disease that America has suffered in recent years."

Inflation climbed somewhat faster in the Washington area, where consumer prices rose by 0.9 percent in December and January, equivalent to an annual increase of 5.6 percent. Details on Page C11

A sharp drop in gasoline prices, declining prices for new cars and clothing all helped to limit the rise in the national consumer price index last month, the Labor Department said. Food prices, however, rose 0.7 percent in January, a bigger increase than in previous months.

The January CPI "continued the price slowdown evident since October," the department said. Inflation has come down significantly over the past year so that prices in January were 8.4 percent higher than a year earlier, compared to an 11.7 percent price increase in the 12 months to January, 1981.

The actual index number for the CPI in January was 282.5, the Labor Department report showed. This means that goods costing $10 in 1967 would have cost $28.25 last month. Social Security and other benefits tied to the CPI will likely rise much less this year than last, as a result of the slower increase in prices.

Most economists expect the improvement to continue during 1982. President Reagan forecasts inflation of 6.6 percent this year.

However, many analysts believe that the slowdown in inflation has been achieved at the cost of the present deep recession and rise in unemployment. Reagan has promised faster growth as well as slower inflation. White House communications director David Gergen said yesterday that the president's economic program is "the major factor" in reducing inflation but he asserted it is not the major cause of recession and high unemployment.

Gergen conceded after repeated questions that White House policies may not be "blameless" for the recession but said "the important message is that over the long haul inflation is coming down." He cautioned, however, that there may be future monthly increases in the CPI that are larger than January's 0.3 percent rise.

Meanwhile, presidential adviser Murray L. Weidenbaum told a group of business executives in New York that this quarter would mark the bottom of the recession and there would be signs of economic recovery by the spring. The president recently backed away from firm predictions of when the recovery would start, saying at his press conference last week, "I'm not going to be pinned down on a date."

Higher than expected interest rates have led several private forecasters to lower their predictions for the economy in the first part of this year. Many economists claim that interest rates have been held up by the prospect of future large budget deficits. Treasury Secretary Donald T. Regan, who earlier said that budget deficits have no impact on interest rates, yesterday told a Senate panel that money markets "are frightened by the high deficits" in Reagan's fiscal 1983 budget.

However, Regan blamed the increase in rates from December to the middle of this month on a surge in the money supply. He said the rate rise was "solely due to monetary concerns rather than fiscal concerns."

Federal Reserve Chairman Paul A. Volcker has argued repeatedly that Congress must cut the deficit in order to bring down interest rates. Yesterday, appearing before the same group as Weidenbaum, he again called for lower deficits and said that "given reasonable confidence in the success of an anti-inflation program today's bond market would appear to offer extraordinary investment opportunities."

Regan said that the slight decline in interest rates in the last few days could signal the beginning of a sustained drop in rates. He agreed with Weidenbaum that growth in the second quarter of this year will show a "plus," and repeated an earlier call for the Fed to allow monetary growth at the upper end of its target range for this year.

High interest rates have hit the housing industry particularly hard, and yesterday the National Association of Realtors reported a drop in home sales in January to an annual rate of 1,820,000 units, the lowest level in a decade.

Other details from the government's January consumer price report included:

* A rise of 0.4 percent in the adjusted inflation index that uses a "rental equivalence" measure to gauge housing costs. Over the year to January this index climbed 8.2 percent.

* A rise of 0.8 percent in the cost of medical care. This has been one of the fastest increasing parts of the CPI, rising recently at about 1 percent a month.

* A 0.7 percent rise in prices for entertainment.

* A drop of 0.2 percent in the index of transportation costs.