Consumer prices rose at an annual rate of 4.4 percent last month, the lowest increase since July, 1980, the Labor Department reported yesterday.

The Consumer Price Index rose 0.4 percent in October, with the improvement primarily the result of a steep drop in housing prices and a decline in mortgage interest rates. The October index was 279.9.

The price report came as interest rates continued to fall. Chase Manhattan Bank dropped its key prime lending rate to a 12-month low of 15 3/4 percent, and other major banks moved down to 16 percent from 16 1/2 percent. Short-term interest rates have now been falling swiftly for several weeks, and market analysts predict that the prime rate will go lower this year.

For most of the summer the prime stayed at 20.5 percent, close to the record peak of 21.5 percent reached in December, 1980. Short-term rates, however, have now come down substantially, with the federal funds rate that banks charge each other for overnight loans down to as low as 12 percent yesterday. The bond market has also started to revive.

The day's economic news triggered a rally on the stock markets with the Dow Jones Industrial Average closing up 18.45 points. Details, Page D7

However, the good news on inflation and interest rates comes partly at the cost of a deepening recession. The sustained period of record high interest rates this summer plunged the economy into recession. And as the recession has deepened in recent weeks, private sector credit demand has fallen off and brought interest rates down.

Housing has been one of the industries hardest hit by high interest rates and recession. Yesterday's price report showed a 0.7 percent drop in house prices in October. This helped to keep the overall housing component of the CPI level with the previous month.

The modest October increase in the CPI followed a jump of 1.2 percent in September. The October figure was the lowest monthly increase since July, 1980, when the economy was in the depths of the last recession. But the October rise is an "aberration on the low side," Commerce Department economist Theodore Torda said.

The underlying level of inflation is "still in the range of 8 to 9 percent" a year, he said. Other administration officials pointed out that so far this year, prices have risen at an annual rate of 9.6 percent, well below the 12.4 percent increase during 1980. The administration's forecast of a 9.9 percent overall price rise for 1981 was "looking good," an official said yesterday.

The president's chief economic adviser, Murray Weidenbaum, "expressed optimism" that the October increase indicates economic improvement "in the months ahead," a White House spokesman said.

The present Consumer Price Index has been widely criticized for exaggerating changes in costs of home ownership, and therefore overstating the rate of inflation. The Bureau of Labor Statistics intends to change the index to reflect the "rental equivalence" of owning a home.

This change, however, would have led to a bigger increase in the October price report. An index using rental equivalence is now published by the department alongside the official CPI. It rose by 0.7 percent last month, compared to 0.4 percent in the offical CPI. In the year ending in October the CPI was up by 10.2 percent, however, compared to 9.1 percent on the new measure.

A grim indication of how swiftly the recession is spreading throughout the economy came with another government report yesterday that orders for durable goods plummeted by 8 percent last month. This was the sharpest monthly drop in factory orders since April, 1979, when a nationwide truckers' strike affected the figures, officials said.

Robert Ortner, chief economist for the Commerce Department, said the drop suggested that industrial production would weaken further in November and December.

Yesterday's price report also showed transportation and medical care costs continuing to rise rapidly, with increases of 1.2 percent and 1 percent respectively. Food and drink prices were up by only 0.2 percent.

The release of the Washington area consumer price report was delayed until today because of the government shutdown Monday.