Several major banks cut their prime lending rate by half a point to 10 1/2 percent yesterday, responding to continuing progress against inflation. The Labor Department reported yesterday that tumbling oil costs helped to hold consumer price inflation to a modest 0.2 percent in January.

The decline in the prime rate brought it to its lowest point in more than four years. The rate had been at 11 percent since early January, and banks had come under growing pressure from Congress and the Reagan administration to reduce lending rates.

The small increase in the consumer price index left that inflation measure still almost as low as it was last September and only 3.8 percent higher than it was in January 1982. The index was unchanged in November and fell 0.3 percent in December.

Inflation in the Washington metropolitan area rose only 4 percent during the 12 months ending in January, the lowest rate for more than a decade. Details on Page D9.

Nationally, the January increase stayed low even though the Bureau of Labor Statistics, as announced earlier, changed the home ownership component of the CPI by substituting a rental equivalence measure for home purchase and financing costs. On the old basis, the January rise was only 0.1 percent and the 12-month increase only 3.6 percent.

First National Bank and Trust Co. of Chicago, the nation's eighth-largest commercial bank, led the way in cutting the prime rate. William McDonough, its chief financial officer, said ebbing inflation, a lower cost of funds for the bank, and an expectation that the economic recovery will increase corporate profits, and therefore reduce loan demand, all contributed to the decision to reduce the prime.

Banks use the prime rate as a reference point in setting the floating rates normally charged on industrial and commercial loans. In many cases, large creditworthy corporations can borrow at rates below the prime, while smaller business usually pay more than prime. Consumer loan rates, which also are coming down slowly, are usually for longer periods than business loans and carry fixed rates.

In recent days, President Reagan and other administration officials have criticized banks for holding the prime rate and their consumer loan rates unusually high relative to inflation and to the rates set directly in the money markets, such as those on Treasury securities.

Both short-and long-term money market rates generally have declined this week, primarily because participants in those markets no longer are as worried as they were that the economic recovery now under way will cause inflation to rebound, financial analysts said.

"Two weeks ago, the markets were deathly afraid of reflation," said economist Charles Lieberman of Morgan Stanley & Co. Since then, world oil prices have begun to fall and "market psychology is greatly improved. . . . Everything is working out. The inflation news is great," he said.

Martin Feldstein, chairman of the Council of Economic Advisers, told reporters that the recovery "does seem to be moving along at a better pace" than was forecast by the administration. Feldstein called the January CPI report "very gratifying news" that underscores the progress against inflation.

Feldstein added that the drop in the prime rate brings it "in line where other interest rates are," with a spread of about 2 1/2 percentage points between the prime and money market rates with which it is related.

The Labor Department said the newly modified version of the CPI rose 0.2 percent both before and after seasonal adjustment. Gasoline prices fell 3.3 percent last month and were down 10.6 percent from their peak in March 1981. Prices for home heating oil fell about 2 1/2 percent.

Meanwhile, grocery store prices were unchanged for the month after declines in November and December. Over the last 12 months, food and beverage prices rose only 2.6 percent.

Medical-care costs continued their upward spiral, rising 0.8 percent in January and 11 percent over the year.

Housing costs, figured on the new basis, rose 0.5 percent for the month compared with declines of 0.8 percent in December and 0.2 percent in November. Calculated on the old basis, housing costs rose 0.1 percent in January compared with the officially reported one-half percent.

Janet Norwood, commissioner of labor statistics, called the change in the home ownership component "an important improvement." BLS has been trying to make the shift "for over 10 years, and it will provide a more accurate reflection of consumer price changes," Norwood said.

The old approach included figures for changes in the full purchase prices of homes and for total mortgage interest costs over half the life of the mortgage. Increases in purchase prices, partly related to houses as an investment rather than just as a place to live, tended to exaggerate CPI increases in recent years. Similarly, the ups and downs of mortgage interest rates also magnified changes in the CPI.

The new approach concentrates on calculating home ownership costs by measuring the cost of the shelter rather than the cost of the total investment. "We do this by using the rent that the owner would have to pay in order to rent a home in the same location as he now occupies," Norwood explained. As a result, home ownership costs now represent only 14 percent of the total market basket of goods and services covered by the CPI, down from 25 percent.

Energy costs make up 12.4 percent of the index, and despite rapidly rising natural-gas prices, they fell 1.3 percent in January. Over the last year, they are down one-half percent. For all the items in the CPI other than energy, prices rose an average one-half percent in January and 4.3 percent for the last year.