Three dozen major banks across the United States yesterday boosted their prime lending rates a full percentage point to 15 1/2 percent, signaling an abrupt end to the one-day stock market rally that followed Ronald Reagan's election on Tuesday.

Although a continuing trend toward higher interest rates had been forecast widely, brokers said fears that stock prices now are headed lower for some time caused many investors to sell yesterday. As measured by the Dow Jones average of 30 industrial blue chips on the New York Stock Exchange, stocks plummeted 17.75 points to 935.41.

It was the biggest single-day decline since an 18.70-point setback last Sept. 29, and it more than obliterated the 15.96-point gain during post-election euphoria on Wednesday, which was the busiest day in Wall Street history.

Volume yesterday was down substantially to 49.16 million shares on the NYSE, compared with the record 84.08 million in the previous session. Composite volume was 56.17 million.

One important beneficiary of the soaring interest rates was the U.S. dollar, which continued to gain strength yesterday against most foreign currencies. And gold prices continued a downward slide of recent weeks, falling $23 an ounce in New York.

But there was growing concern that the bond market may be headed for another severe crunch, because of the rise of interest rates toward historic highs. Bond prices fell more than a point yesterday, and dealers said demand was weak for the federal government's 3 1/2-year notes sold Wednesday, even though the yield was a record 13.31 percent.

Yesterday, the Treasury offered another record rate to investors -- 13.07 percent on $2.25 billion of 10-year notes, well above the previous auction when the yield was 10.81 percent. [Story on Page E3]

Some analysts are warning that the interest rate spiral is threatening the recovery from recession evident in recent months, but William Sullivan Jr., senior vice president at the Bank of New York, said that based on the current cost of funds to banks "a 16 1/2 percent prime is justified right now in short-term rates in the near future."

Most brokers and dealers expect the Federal Reserve Board to boost the basic discount charged to member banks in the next day or so by 1 percentage point or more above the current 11 percent level.

All of these developments are sending shudders through the real estate and home building industries, since mortgage rates now are starting to hit the 15 percent range and construction loans generally are 2 percentage points above prime.

"This is bad news for the housing industry, there's no question about it," said Michael Sumichrast, chief economist for the National Association of Home Builders here. A 15 percent mortgage "disqualifies almost 95 percent of American households from obtaining a loan," he added.

The prime rate increase was initiated early yesterday by Chase Manhattan Bank of New York, the nation's third-largest. By late yesterday, more than 30 big banks had joined in hiking the prime by a full percentage point, including No. 1 Bank of America, Manufacturers Hanover Trust, Morgan Guaranty, Chemical Bank, Bankers Trust, Crocker National, First National of Chicago and Continental Illinois.

Riggs National Bank, the largest in metropolitan Washington, raised its rate to 15 1/2 percent, effective today. "I don't see any great decline in interest rates for the balance of the year, because I see no facts that would suggest they could go down," said Riggs Chairman Vincent Burke Jr., who agreed that the current interest rate environment effectively has shut down once again the real estate sales business here.

"The cost of funds to banks has risen sharply in recent weeks," said Chase, in a statement. "Indeed, this increase does not fully reflect the increased cost of funds to Chase." Even as the banks were posting the higher primes, federal funds were trading at 15 1/2 percent and higher. These funds, traded overnight among banks, are one source of a bank's resources.

Banks also started paying about a full percentage point more yesterday on a six-month savings certificates, adding other pressures on the banks, which have boosted the prime rate 3 1/2 percentage points in the last three months. Some banks, including First National Bank of Boston and Riggs, have reinstated lower prime interest rates for qualifying small businesses.

Although President-elect Ronald Reagan was not asked about interest rates at his news conference in Los Angeles yesterday, he did vow to move "as quickly as possible" to implement such promised policies as a tax cut and said he would support action on his plans by the lame-duck session of Congress, which returns to town next week.

Sen. Robert Dole (R-Kans.), the future chairman of the Senate Finance Committee, later told reporters he favored action on a $39 billion tax cut in the next few weeks, a move brokers said would encourage equity investments in corporations poised to expand and modernize plant and equipment.

But the mood among investors yesterday was bearish. Of the 15 most active NYSE issues, only LTV Corp. and General Dynamics advanced. LTV was the volume leader, up 7/8 to 15 1/8. Dynamics, a diversified defense and electronics firm that did not trade at all on Wednesday because of an imbalance of orders, jumped 3 to 71. One local gainer for the second day was Fairchild Industries, up 1 3/4 to 31.

Elsewhere, of 1,937 issues traded, 1,390 declined and only 257 advanced. The New York Stock Exchange composite index fell 1.35 points to 74.29, and the Standard & Poor's index gave up 2.42 points to 128.91. The impact of the 15 1/2 percent prime rate was similar at the American exchange and in the over-the-counter market. The Amex index fell 6.56 points to 332.25, while the NASDAQ composite index of OTC stocks fell 2.07 points to 193.96.

All sectors of the market declined, including most of the defense and energy issues that had bounced higher after the GOP landslide. International Business Machines fell 2 to 66 1/2, and Mobil Corp. was off 2 1/8 to 73 1/2. Precious-metal stocks fell, reflecting flagging interest in gold and silver. Among active OTC stocks, MCI Communications of Washington fell 1/8 to 13.

The dollar's strength was universal, buttressed by the rising interest rates here and the expectation that a new Republican administration will follow policies of fiscal restraint. In turn, the dollar's strength helped pull investors out of gold, the price of which plummeted $23 to $615 an ounce in New York.

"The Federal Reserve has been making a one-pronged attack on inflation," said Marc Berkowitz, chief trader for James Sinclair & Co., explaining some of the flight from gold to the U.S. currency. "Now the Fed should have the backing of the legislative and executive branches in taking the necessary steps to reduce government spending."

In Frankfurt, the dollar rose to 1.9460 marks from 1.9360 marks, and it rose to 1.9490 in New York. In Zurich, the close was 1.7445 Swiss francs, up from 1.74075. Dealers in London told Dow Jones News Service that the dollar's rise wasn't as great as it might have been, considering the sharp prime rate hike, and they said there was "substantial" market intervention by West Germany's central bank, the Bundesbank, to slow down the dollar's upward trend.

The gold settlement price on the Comex in New York was $613.30 an ounce, down from $637, but a Comex trader told United Press International that November contract trading was completely inactive. Gold fell $20 in Zurich to $632.50 a troy ounce and by $23 in London to $625.50. Silver declined in New York to $18.70 from $19.10 on Wednesday.