The number of homeless families who sought emergency shelter in Washington doubled to 96 last month -- the biggest monthly increase in memory -- and the rate is accelerating even more this month, city officials said yesterday.

"We were very surprised," said Patricia Yates, chief of the social services division of the D.C. Department of Human Services, who blamed the deterioration of the economy and the lack of affordable rental housing for the increase.

But the suddenness and dimension of the increase has left DHS officials puzzled, she said. "It's very weird," she said, "We are trying to figure it out. We are reviewing the cases" to pinpoint a cause.

"It is too early to tell whether this is a freakish phenomenon based on something we can't yet get our finger on, or whether it reflects what will be a new, continued big problem for the city," Yates said.

Several housing and welfare specialists speculated yesterday that the increase might be the result of Reagan administration cuts last winter in various entitlement programs, but Yates said interviews with homeless families failed to support that.

Last year, the city temporarily housed 406 families at its two family shelters, but expects the figure this year to top 700, Yates said. The monthly intake of new families had been averaging 40 to 50 until the July increase, she said.

The city will exceed its $1.2 million yearly budget for emergency family shelter, Yates said, though it is unclear by how much. "We are spending money at a very fast rate," she said.

The city pays $34 to $40 a day for motel rooms for homeless families, plus $10 to $12 per person per day for cafeteria-style meals. Homeless families are sheltered at the 47-unit Pitts Motor Hotel at 1451 Belmont St. NW and, under a new contract signed by DHS last month, at the 200-unit Capitol City Inn, formerly the Diplomat Motor Hotel, at 1859 New York Ave. NE.

In addition to the increase in numbers, the average length of stays in the temporary shelters has steadily increased, Yates said. Since the city started its emergency family shelter program in 1965, the average stay generally has been two to three weeks, she said. This year, the average is 30 to 35 days because of difficulties in finding suitable housing, she said.

Public housing, the normal refuge for the homeless, has a waiting list of about 7,000 families, many of whom have waited for years for accommodations. In addition to family shelter, the city also runs dormitory-style shelters for homeless men and women.

About half the families seeking shelter were evicted from their previous quarters, most of them for non-payment of rent, Yates said, while others are homeless because of fires, violence within the family or overcrowding.

"People just can't pay the rent," said Etta Horn Prather, director of the D.C. Citywide Welfare Rights Organization in Southeast, who said her advocacy group is reporting increasing numbers of welfare recipients who face eviction because of delayed welfare checks or cutoffs of various benefits.

Lynn Cunningham, a housing specialist with Neighborhood Legal Services Inc., said that many welfare and food stamp recipients whose benefits were reduced last winter may only now be facing eviction. Cunningham said the city averages about 100,000 eviction notices annually, with about 4,000 evictions actually occurring.

Yates said the budget overrun may force DHS to reevaluate the shelter program. Last April, in settling a lawsuit in the U.S. Court of Appeals, DHS and other city officials agreed to set up a Commission on Homelessness to study the problem. That commission is in the process of being established, according to Ilene J. Jacobs, an attorney for the National Housing Law Project.

At the Capitol City Inn, manager Thomas Kirland said that city officials told the motel's owners, K & K Management Inc., that they planned to use 15 rooms in early July, and 40 by month's end.

Instead, he said, the number of rooms used quickly climbed to more than 100. "We had 111 rooms used by the city last night, and we had 311 people eating," he said. "I was shocked. I didn't realize there were that many homeless people."