Bad weather and the still deepening recession pushed industrial production down 3 percent last month, the sixth consecutive monthly decline and the worst for a single month since January, 1975, the Federal Reserve reported yesterday.

Since last July when the recession began, output at the nation's factories, mines and utilities has fallen 9.6 percent on a seasonally adjusted basis to a level 1 percent lower than the bottom of the 1980 recession.

Automobile assembly plunged 22 percent to an annual rate of only 3.6 million vehicles, the lowest rate in more than 20 years.

The Commerce Department, meanwhile, said new housing starts fell slightly in January to a seasonally adjusted annual rate of 894,000 units. It was the sixth month in a row in which the rate was below 1 million, but some housing industry analysts took heart from a 6 percent rise in building permits last month. They also are encouraged that the level of new starts in December and January combined were at an annual rate about 40,000 units higher than in October and November.

But lower interest rates are the key to any significant rebound in housing construction, and interest rates are rising. Major banks across the country raised their prime lending rate yesterday from 16 1/2 percent to 17 percent in the wake of a general increase in short-term interest rates in money markets. Story on Page D9

With interest rates continuing to go up, a number of economists are revising downward their forecasts for 1982. Walter W. Heller of the University of Minnesota and George L. Perry of the Brookings Institution, in a joint forecast released yesterday, said the decline in gross national product this quarter should come close to last quarter's 5.2 percent annual rate. Real GNP will continue to fall at a 1.7 percent rate next quarter as well, they said.

The unemployment rate will rise to about 10 percent next quarter before the economy turns up modestly later in the year, according to Heller and Perry. By the end of the second quarter of this year, they added, real output will be below its level of three years ago.

"Not since the depression of the 1930s have we seen a span of three years with no net advance in real GNP," they said.

Most other forecasters expect the recession to end somewhat sooner than Heller and Perry, but others, too, expect a slower recovery than the 5 percent real increase the Reagan administration is predicting. For instance, Jerry Jasinowski, chief economist for the National Association of Manufacturers, said high interest rates will mean a slower-than-normal rebound in sales of durable goods, such as autos.

Part of the big decline in industrial production last month was due to unusually bad weather in many parts of the country. However, technicians at the Federal Reserve adjusted their numbers to eliminate most of the large decline in the length of the average work week in January, which they believe was weather-related.

The declines in output were widespread, with the largest occurring in autos, construction supplies and materials from which both durable and nondurable goods are made.

Durable goods production, including autos, dropped 5.5 percent. Output of construction supplies went down 4.8 percent, and materials were down 3.7 percent, the Federal Reserve said.

Once again, production of defense and space equipment was the only major component of the industrial production index showing a gain. It was up a scant 0.1 percent.

Frederick Napolitano, president of the National Association of Home Builders, said the January figures for housing starts, which were 44 percent below a year ago, show "the housing industry is at rock bottom and it isn't going anywhere under present conditions and policies." "The administration is counting on housing leading the economy out of this recession, but that's not possible until long-term interest rates decline, the budget deficit is brought under control, and the administration and Congress enact an emergency stimulus program to give the housing industry a much-needed shot in the arm," he declared.