As a human chain of volunteers began unloading food for a Thanksgiving dinner in Lafayette Square yesterday, it seemed that they would outnumber the homeless and hungry they had come to serve. But the word spread quickly that there was food to be had across from the White House, and more than a thousand destitute persons streamed into the park, turning benches, hedge tops and sidewalks into holiday dinner tables.

From heating grates and homeless shelters, those who said they had not eaten a decent meal in weeks mingled in the park with others who felt sorry for them, making for the largest of many Thanksgiving dinners held for homeless people in the city yesterday.

In Anacostia Park, a smaller group of street people turned out for a dinner offered by the Hari Krishnas. In Kalorama Park, about 200 people showed up for a dinner prepared by volunteers.

Many churches held dinners for the down and out. Church buses and soup-line vans were busy throughout the day, making pickups and dropoffs at shelters around the city.

The spirit of the day even extended to the 14th Street red-light district, where "modeling" studio employes collected enough canned goods and cash contributions to prepare 50 dinners and make donations to local churches.

"I just decided there was too many people out here in need," said Larry Humphries, vice president and general manager of two studios. "I did not do this for the business, although I am a politically minded person. These street people have been begging . . . for quarters and dimes for years, so we decided this year to do something for them."

With such an outpouring of good will throughout the District, despair took a backseat to charity, making for a rare cityscape in which many street people seemed to disappear.

But the presence of so many in Lafayette Square rekindled concern among the volunteers that the plight of the poor is worsening. While a day of food-sharing was in the best of American tradition, few thought that it was enough.

"This just goes to show what can be done if people pitch in and come together," said Mitch Synder, head of the Community for Creative Non-Violence, which sponsored the dinner in the park.

"I think this is something that needs to be done every day. This shows that we can count on the human spirit."

Synder was constantly congratulated by the homeless and hungry who recognized him. One carried a sign that read, "I'm thankful for Mitch Synder." Two weeks ago, Snyder ended a 51-day hunger strike after pressuring the Reagan administration to renovate an 800-bed shelter for the homeless at 425 Second St. NW.

Despite the problems of the homeless, there were jovial moments. Some people dined in groups, telling stories about the last time they had eaten so well. Others, shying away behind trees, protected their plates as they took time to savor each morsel.

The sight of so much food had put them on their best behavior, with scores patiently waiting in line with paper plates and plastic forks and spoons.

"I'm thankful for all these fine people who made this wonderful food," said Charles Hicks, 55, who lives at the Blair School shelter for the homeless. "I didn't know what I was going to do for dinner today until I heard about this."

His plate was loaded with turkey, dressing, cranberry sauce and beans. He blessed each forkful, then worked the food around in his mouth as if testing fine wine."Thank the Lord," he said.

Seated alone, another man couldn't stop eating, shoveling down his food in the manner of one who had not eaten in days. "I'm anonymous," he said between bites. "Nobody knows me."

For the volunteers, there was the joy of sharing time and reflecting with those sympathetic to their concerns about the problems of hunger worldwide.

"When you see what's happening in Ethiopia, it makes you want to do something," said Earlene Cole, an employe at the C&P Telepone Company, as she served cranberry sauce. "You have to start somewhere and I say start at home."

"I'm fasting today, like a lot of Indians," said Bridgette Cline, who works for the Folger Theater, as she talked with the homeless about their problems. "I have personal reasons for being here. I just felt I needed to be."

Tom Campbell, a plasterer from London vacationing in Washington, said he came out to volunteer because "I thought this would be a good way to spend Thanksgiving. I have other things planned, but I wanted this to be a part of my day."

Maxine Schutter, a social worker in Virginia, said she heard about the dinner from the Ethical Society of Washington. "They said they needed volunteers and this sounded like a good cause."

"I can't thank them enough," said Acie Jones, 65, a retired clerk who lives in a city shelter. "I've never gone hungry. If you can keep up with people like these [volunteers] , get on their schedule and know when they are going to help out, you can do pretty good out here."