Signs that the long-awaited drop in interest rates may be under way at last came yesterday as major New York banks dropped their prime interest rate to 19.5 percent and the Federal Reserve Board cut one percentage point from its penalty surcharge levied on frequent borrowers from the central bank.

At the same time, the interest rate which the Treasury Department has to pay on funds it borrows dropped at yesterday's sale of short-term debt, and the stock market rallied to close up 10.37 points at 846.56.

The drop in rates came despite growing uncertainty on Capitol Hill about President Reagan's chances of winning further budget cuts for fiscal 1982. Wall Street fears of a much higher federal deficit have been one factor keeping interest rates at record heights over the summer. The administration's latest push for more spending cuts is partly designed to calm the markets and bring interest rates down.

However, experts have been predicting that rates would fall somewhat as the economy slows and private demands for credit are choked off. This slackening in the private sector, together with a recent easing in monetary policy, has enabled rates to slip back from their peaks even though the government's credit demands remain high.

Murray L. Weidenbaum, chairman of the president's Council of Economic Advisers, warned a congressional committee yesterday that interest rates will not come down substantially until inflation is reduced and that only "substantial additional budget reductions" can remove the danger of "crowding out the private sector's legitimate borrowing needs."

Economists yesterday cautioned that rates may not fall far or fast, especially if the administration does not win the new budget cuts that it wants. The Federal Reserve, backed by Reagan officials, is committed to a very tight money policy which it hopes will reduce inflation.

The shortage of credit which this tight policy involves has forced up interest rates and may keep them relatively high for some time, according to Charles L. Schultze, former economic adviser to President Carter.

The Federal Reserve called its action yesterday a "technical response to the decline over recent weeks in short-term money market rates."

The surcharge on the discount rate was lowered from four percentage points to three percentage points, effective Oct. 1.

The basic discount rate charged to borrowers from the Fed's "discount window" was left unchanged at 14 percent, where it has been since May.

Changes in the discount rate generally follow rather than lead the market, but they sometimes encourage other rates to move.

The Federal Reserve has been trying to encourage a little faster growth in money in recent weeks, to make up for a long period when the money supply was growing below its target range. However, the central bank has moved cautiously for fear of pumping too much money into the economy.

Chase Manhattan, the nation's third largest bank, led the way with yesterday's half point drop in the key prime rate. It was quickly followed by other New York and Chicago banks.

The fall came just one week after an industry-wide drop in rates to 20 percent from the 20.5 percent where they had stood since early July.

The prime rate still stands very high in relation to the underlying rate of inflation, which most analysts now believe is running at 8 percent to 9 percent.

It is also high relative to the cost of short-term funds which the banks must borrow. These have declined about 4 percentage points this month, but banks have been reluctant to drop the prime in case the short term rates started back up.

Weidenbaum admitted that the much higher than forecast interest rates so far this year have added to federal spending, but said that the administration was not going to revise its economic forecast now. He told the budget panel that Congress had overspent by $6.1 billion from the president's request for 1982.

However he declined to give details of where the administration believes the extra spending is, except to say that $800 million comes from differences in the Medicaid program.

Budget Committee Chairman James R. Jones (D-Okla.) said that higher than anticipated interest rates already had added $10.3 billion to the budget for 1982, and rates might be higher in 1983 and 1984 thus throwing off the projections for those years as well.