THE leaves of Lafayette park are curling and falling, exposing the White House across Pennsylvania Avenue. Linda sits on a wooden bench, wrapped in several layers of tired clothing, tossing bread bits to pigeons and scolding a few sea gulls for taking more than their fair share.The park is a regular stop on Linda's daily route through soup kitchens and shelters for the homeless, the "necessary evils" she relies on to fend off the first cold snaps of winter. She has lived on the streets here for more than two years, waiting for public housing in a system long backlogged. The problem that keeps Linda homeless is acute. Lack of affordable housing, advocates say, is the primary cause of homelessness in big-city America. A study released last week shows its even worse for the homeless mentally ill. The survey of the 22 largest cities by the United States Conference of Mayors found that: * Roughly one-third of homeless people in the cities studied suffer from severe mental illness, and about half of those are also addicted to drugs and alcohol. The number of mentally-ill homeless has increased by 7 percent since January 1990; the number of those who also are addicted to drugs and alcohol increased by 9 percent. * Eighteen cities cited the lack of affordable housing as the primary cause of homelessness among the mentally ill. Other reasons include lack of income and supportive services. * While requests for emergency shelter by the homeless mentally ill are increasing, the number of beds available is decreasing. * Half the survey cities reported a 35 percent increase in requests for emergency shelter of the homeless mentally ill. Shelters must turn away persons in two-thirds of the cities. At a press conference here last week, Boston Mayor Raymond Flynn, president of the conference of mayors, told reporters: "For too long, ending homelessness has not been a federal priority. And state governments, even when they have tried, have fallen short." While the mayors' study is an indicator of the growth in homelessness in America, the scope of the overall problem is difficult to ascertain. The 1990 US census counted 228,621 persons in shelters and on city streets. Critics of that figure estimate the homeless count falls between 500,000 and 5 million persons. The mayors estimate that about 206,000 persons in the 22 survey cities are homeless. More certain is the need to increase and link housing and services. By extrapolating statistics from a US Department of Housing and Urban Development (HUD) study submitted to Congress in June, MaryAnn Russ, executive director of the Council of Large Public Housing Agencies, estimates that 600,000 new and modernized housing units are needed. Recent appropriations for fiscal year 1992 are adequate to fund 7,500 housing units, the level required by the 1990 National Affordable Housing Act. Congress has increased appropriations in 1992 for the McKinney Act, which provides a wide range of programs and benefits for the homeless. Nonetheless, without adequate housing, providing services is difficult. "Most homeless can function successfully in housing, if an effort is taken to secure services," says Ms. Russ. But "HUD has never asked for full funding [for new housing], even though [President] Bush campaigned on full housing. That promise has been broken."