Single-family home starts plunged to their lowest level on record in October, and starts for all types of housing dropped to a 15-year low, the Commerce Department announced yesterday.

Housing economists said yesterday that the depressed market has not hit bottom yet, however, as evidenced by a sharp new decline in the number of building permits being issued, and they said a recovery in the housing industry cannot begin before February or March.

Total starts were at an annual rate of 857,000 for October, only slightly higher than the 843,000 rate recorded in October 1966, the only month with a lower figure since the Commerce Department started collecting the data in 1959. The actual number of starts for the month was a mere 86,200, about 43 percent less than in October 1980. Three years ago, starts peaked at an annual rate of more than 2 million.

The low starts also are having a ripple effect on the economy as a whole that has not yet shown up in official figures such as unemployment rates, loan delinquencies and lenders' profits, economists noted.

"I don't think the housing industry can start to recover for another three to four months," said Michael Sumichrast, chief economist at the National Association of Home Builders. The industry is "too decimated, there is too much inventory," he added. "You can't turn it around."

But a top administration housing official predicted a rebound will start "in the weeks ahead" because of recent drops in interest rates. Philip Winn, assistant secretary for housing at the Department of Housing and Urban Development, said the home-start figures, "while disturbing news to this de partment . . . should be considered in the context of recent positive indicators which truly reflect the very beginnings of an upturn in housing."

Single-family homes were started at a 487,000 annual rate, which the homebuilders association says is 20 percent below the previous all-time bottom of 612,000 units.

The housing industry has been in its longest and deepest slump since the Depression, and home starts for all of 1981 will be at or below the 1.023 million rate for 1946, which marks the country's postwar low for an entire year.

Sumichrast said the two positive signs now are that interest rates have started to decline and personal income figures released by Commerce yesterday were up. If interest rates continue to fall, a "shallow recovery" could begin in February or March, with slow improvement following, he predicted.

Mark Riedy, vice president of the Mortgage Bankers Association, said starts for November probably will be below an annual rate of 800,000. "Whether November will be rock bottom, I'm not sure," he added.

Riedy also predicted there can be no "fast snapback" for the housing industry even if rates continue to fall. "It's gone too far. . . . With people out of business and profit margins totally destroyed, the industry loses its resiliency," he said.

Building permits for housing construction declined in October to an annual rate of 729,000 units, 14 percent lower than revised September figures and 46 percent below the rate one year ago.

Riedy said figures to be released soon by the Mortgage Bankers Association also show record-high delinquency rates. Builders are starting to have such problems with their construction loans that they are telling lenders to go ahead and foreclose on unsold homes, he said. But lenders can't sell these homes either, so they aren't foreclosing but are losing money on the delinquencies, Riedy added.