New housing starts dropped 6 percent in January to a seasonally adjusted annual rate of 1,420,000 units, the lowest level since 1976, the Commerce Department reported yesterday.

As rising mortgage interest rates push homes beyond the ability of many families to buy, sales of both existing and new houses have been falling, causing homebuilders to cut back construction plans.

The U.S. League of Savings Associations, which represents more than 90 percent of the nation's savings and loan associations, said the level of new mortgage loans closed last month fell to only $3.7 billion, down from $6.6 billion in January 1979, and nearly $7 billion in January 1978.

In addition, William O'Connell, executive vice president of the U.S. League, said commitments for new homes loans declined by $500 million last month.

"In the last four months, commitment levels have fallen $6.8 billion, or 30 percent, in direct response to tight monetary policies adopted by the Federal Reserve Board," O'Connell said. Mortgage rates are edging closer to 14 percent in some parts of the country, according to the League.

Sepearately, the Commerce Department also reported yesterday that personal income of Americans rose $11.4 billion, or 0.6 percent, in January to a seasonally adjusted annual rate of $2,036 trillion. It was the smallest monthly increase since last May.

In an unusal development, however, disposable personal income rose by more than personal income. Disposable personal income is what is left after personal tax and nontax payments, such as for Social Security, and except when there is a tax cut usually rises by less than does personal income.

Last month the turnaround came because the federal government began issuing income tax refund checks at a $10 billion annual rate because of overwithholding during 1979, the department said.

Meanwhile, personal outlays rose by 1.2 percent for the month, the same as the increase in disposable personal income. But as outlays climbed to an annual rate of $1.623 trillion, the department said the personal savings rate continued to drop.

Commerce prefers to calculate the savings rate only as a three-month average, and on that basis said it dropped to 3.2 percent of disposable personal income in December. However, other figures indicate it fell below 3 percent in January, a level unmatched since the Korean war buying spree in 1950.

Consumer prices, as indicated by the deflator for personal consumption expenditures -- which some economists believe is a better measure of inflation than the consumer price index because of the way the CPI treats housing costs -- rose 0.8 percent in December compared to 1.1 percent for the CPI.

With Federal Reserve Chairman Paul Volcker announcing yesterday that the Fed would continue to keep a tight rein on credit availability this year, analysts said the outlook for housing finance was bleak.

Volcker was challenged on this point at a hearing of the House Banking Committee, and responded by saying the real culprit was high inflation rates which have led to high interest rates. The Fed chairman also rejected a suggestion by one member of the committee that the Fed impose credit controls so that interest rates could be lowered, with housing getting the benefits.

Much of last month's drop in new starts occurred in multifamily structures. Starts of buildings with five units or more dropped from a 371,000-unit rate in December to a 287,000 rate in January. As recently at last September, the rate of such building starts was running above 500,000 units.

Single-family houses were started at a 988,000-unit rate in January, down about 20 percent from last June.