A series of fresh government statistics showed a visible weakening last month in several key sectors of the economy, suggesting the long-predicted recession finally may be beginning in earnest.

The Commerce Department reported that housing starts plummeted last month as skyrocketing home mortgage rates put purchases beyond the reach of many buyers. Overall starts fell 6.3 percent to a new annual rate of 1.3 million units.

At the same time, the department said consumer spending fell off noticeably during the month as Americans' personal income rose decidedly more slowly. In the only good news of the day, the agency reported business inventories remained lean.

The figures came as, separately, several of the nation's major banks pushed their prime lending rates charged to creditworthy corporate customers to 19 percent from 18 1/4 percent.

The new signs of heightened economic slowdown generally were welcomed by the Carter administration, which is seeking to dampen consumer spending in an effort to help slow the inflation rate.

Courtenay M. Slater, the Commerce Department's chief economist, said the statistics were in line with predictions of a mild recession. Slater noted that the continued lean inventory holdings make a serious downturn still unlikely.

The sharp plunge in housing starts virtually paralleled the recent surge in home mortgage rates and came almost entirely in single-family house construction which declined 23.1 percent over the month.

Inexplicably, starts of multifamily units rose 34 percent in February, with a particularly sharp increase in apartments with five or more units. Analysts said the figures may have been distorted by seasonal adjustment.

Overall housing starts now are running 9.2 percent below their rate of February 1979. The department also reported a 7 percent decline in permits for new construction. Permits for single-family homes were down 26 percent.

Sharon L. Steiber, economist for the Federal Home Loan Mortgage Corp., called the February decline "expected" in the face of soaring interest rates. "Few households can qualify for a mortgage at current mortgage and home prices," she said.

The figures on consumer spending showed personal consumption outlays rose 0.5 percent in February, after increases of 1.5 percent in January and 1.3 percent in December -- the first serious slowing in the several months.

The personal income of Americans rose 0.3 percent, or $6.9 billion, last month to a new seasonally adjusted annual rate of $2,052 trillion. Personal income rose 0.8 percent in January and 1.1 percent in December.

The bulk of the slow-down in income growth came in the farm sector. Factory payrolls rose 0.7 percent in February -- about the same as January's 0.6 percent rise, but well below December's jump of 1.2 percent.

Income from interest and dividends also rose sharply, but income from transfer payments fell one percent over the month after rising 2.3 percent in January. Income levels have risen quite rapidly until only recently.

The figures on inventories showed stockbuilding by businesses rose 0.9 percent, or $3.86 billion, in January to a new seasonally adjusted $432.27 billion. The rise compared with an 0.2 percent increase in December.

However, trends in specific sectors of the economy were widely disparate, with retail inventories plunging 1.1 percent, after falling 1.3 percent the previous month, and manufacturers' inventories leaping 1.8 percent.

Despite the overall increases, the closely watched ratio of inventories to sales dipped to 1.38 months' stocks in January from 1.41 months in December -- indicating inventories still are lean and are not a threat to the economy.

Rapid inventory-building in early 1974 was cited as a major factor contributing to the 1974-75 recession. When businesses accumulate excess inventories they have to cut purchases when a slump comes and the downturn becomes worse.