Factory use by U.S. manufacturers fell to 71.1 percent of capacity in April from 71 1/2 percent in March, matching the lowest rate since the severe 1974-75 recession, the Federal Reserve Board reported yesterday.

The new figures, coupled with other reports showing industrial production dropping and unemployment rising in April, indicated strongly that the recession still was worsening as the spring quarter got underway.

The new report said manufacturers also had operated at 71.1 percent of capacity in January, but many economists believe that figure was held down by unusually bad weather.

The last time the rate was lower was in May 1975, when it was at 70.3 percent.

On a more hopeful note, the new Fed report said that "during March and April, the manufacturing and materials operating rates declined less rapidly than they did from September 1981 through January 1982."

Meanwhile, in a separate report issued from New York, the F.W. Dodge division of McGraw-Hill Inc.'s forecasting unit said construction of housing declined 33 percent to 192,596 units during the first quarter from 288,231 a year ago.

"Ordinarily, when the economy is as deep into recession as it is now, funds that are not being invested in the industrial sector find a secondary outlet in residential building. Since the housing market hit bottom last summer, however, the sustained high level of mortgage rates has blocked its recovery," observed George A. Christie, vice president and chief economist for F.W. Dodge.

The Dodge report showed that, after adjustment for seasonal variations, the first-quarter figures were down 3 percent from the final 1981 quarter.

The nation's 10 leading housing areas during the first quarter of 1982 were Houston, Dallas, Phoenix, Atlanta, Tampa, Los Angeles-Long Beach, Washington, Denver, Ft. Lauderdale-Hollywood, and Miami, Dodge said.

The figures for the last five months, all adjusted for normal seasonal variations, were revised in the new report. And the April rate is also subject to revision when more complete information is available.

Details of the report said:

* The operating rate for motor vehicles and parts increased for the third straight month in April, but the industry still operated at less than 55 percent of capacity.

* Bad times continued in the metals industry, with capacity utilization rates for raw steel and for nonferrous metals down 33 percentage points and 20 percentage points from their levels of one year earlier.

* Factory use for production of industrial materials dropped even lower than for manufacturing, declining from 71.6 percent in March to 70.8 percent in April