Industrial production plunged 1 1/2 percent in October as the recession continued to sweep through the nation's economy, the Federal Reserve reported yesterday.

The drop in output at the nation's factories, mines and utilities was the sharpest for one month since June 1980, when economists were using words like "free fall" to describe what was happening to the economy.

Treasury Secretary Donald T. Regan said in a speech to the Washington Press Club that he expects a "very serious downturn in the real gross national product in the current quarter." After adjustment for inflation, the economy will contract at an annual rate of between 3 and 3 1/2 percent this quarter, Regan predicted, with the decline continuing through the first quarter of 1982, though at a lesser rate. "By the second quarter we'll probably be pulling out of this recession," he continued.

Some economists believe the drop this quarter will be considerably greater, with a few even suggesting this recession will rival that of 1974-75, which was the worst since the Depression of the 1930's. During the 1980 recession, real GNP in the second quarter fell at a record 9.9 percent annual rate, but quickly turned around in the third quarter.

Commerce Secretary Malcolm Baldrige called the production report "another sign that economic weakness in autos and housing has spread across the industrial sector."

As in September, when the industrial production index fell a revised 1.2 percent, last month's 1 1/2 percent drop was the result of a decline in every major category except defense and space. The output of construction supplies plummeted 3.8 percent following a 3.3 percent decline in September. And production of durable consumer goods--primarily autos and home appliances--fell 2 1/2 percent, the fourth consecutive monthly decline.

The production of business equipment went down for the third month in a row, falling one-half percent in October.

There are strong indications that the declines in production are continuing. Automobile manufacturers in particular are slashing their production schedules to try to keep inventories in line with depressed sales. As production is cut, so are the number of employes and their hours of work. Initial claims for unemployment insurance climbed to 550,000 for the week ended Oct. 31, the highest level since July 1980, the Labor Department reported this week.

Despite the efforts of business executives to cut production to keep inventories in line with sales, the stocks of manufacturers and wholesale and retail businesses continued to grow in September. Total business inventories rose 0.9 percent that month to a seasonally adjusted level of $507.21 billion, the Commerce Department said. The increase for August was also revised upward from 0.7 percent to 0.9 percent. At the same time, business sales rose only 0.4 percent in September.

Meanwhile, the Federal Reserve also reported that one measure of the nation's money supply, M1-B, rose $2.2 billion to $433.2 billion in the week ended Nov. 4. However, M1-B--which includes currency in circulation and checking deposits at financial institutions--remained far below the target range set by the Fed. tables on D10

In an effort to boost growth of M1-B, the Fed continued to pump cash into the nation's banking system this week, analysts said. Those actions, coupled with the effect of the recession in slowing the growth of business loan demand, have sent short-term interest rates down sharply.

Several major commercial banks lowered their prime lending rate to 16 1/2 percent from 17 percent Thursday. Nevertheless, several analysts predicted that, although rates will continue to fall for a while, they will rebound once the economy begins to grow again.

The Department of Housing and Urban Development announced yesterday that the maximum interest rate on FHA-insured mortgages for single-family homes would be lowered from 16 1/2 percent to 15 1/2 percent Monday. VA loan rates also will go down Monday.