Annie P. could hardly believe her eyes when she read the letter sent to her by the District of Columbia last December. Annie, 43, unable to work because of illness, was notified that she would no longer be eligible to receive her monthly $478 Aid to Families with Dependent Children (AFDC) check as a result of the Reagan budget cuts.

"I was really shocked when I received that letter," she said. "I have never been in that predicament before." Annie, who had supported herself and six of her children living at home on $696 a month from a combination of food stamps and AFDC, was unable to pay her rent, utility bills, food and medical costs with just $218 of food stamps. Her Medicare did not pay the $50 in medicine needed each month to treat her severe asthma, bursitis and high blood pressure, and the asthma suffered by three of her children.

"I was really hurting. I had no money, not even to buy a bar of soap. I just prayed night after night," Annie recalled. Although she turned to emergency programs for help, all she could get was two food vouchers worth $45 each from the Salvation Army, she said. Concerned friends and neighbors, some economically hard-pressed themselves, loaned her as much as they could.

But today, Annie P. is back on AFDC, which is designed to protect poor children by giving their families income support. After a hearing on her case, officials determined that her elimination from the program had been an error. After three months without income she finally began receiving checks, but for $422, $56 less than she was getting originally. She has not yet begun to repay all her debts.

But Sarah F. hasn't been so fortunate. Cut from AFDC and Food Stamps last December, Sarah has been without any income since. "I'm getting to the point now where I'm getting very depressed and the bills keep mounting up," Sarah said.

Sarah, 36, had to stop working last year because of illness. In and out of the hospital, some times for 30 days at a strech, she depended on the $209 a month to help support herself and her two children. "When you have someone else watching the children and no food at home it hard to sit at the hospital without worrying," she said.

Sarah said she reapplied for AFDC and Food Stamps and was turned down. Although her medical bills were covered by Medicaid, she could not pay her rent and was surviving on the minimal food she was able to get through various social service agencies. Things got so tough, she said, that she even contemplated putting her children in a foster home, but decided not to after learning it would take two to three years to get them back.

"This is enough to drive anyone crazy. Sometimes I just don't know what to do," Sarah said. "We've just been hanging in there. I've never felt so down in my life."

Officials of the agencies involved with the two cases declined to comment on why the women were cut off.

But according to other officials of numerous social services agencies, these cases represent just two of the many families that have been affected in the District as a result of the federal budget cuts imposed last October.

Nationally, out of $50 billion in across-the-board program cuts, $1 out of every $3 spent on children's programs have been or are proposed to be eliminated, according to the Children's Defense Fund (CDF); a Washington-based child advocacy group.

"The Reagan administration has earned a resounding 'F' for its care and concern for the nation's children in 1981 -- a grade it seems bent on repeating in 1982," CDF charged in a report on how the cuts would affect children.

For the District, according to various D.C. officials, these federal cutbacks have affected in varying degrees several key programs for children:

* Aid to Families with Dependent Children (AFDC): Locally, almost 4,200 households have been eliminated from the program since September, mostly because of a new monthly reporting requirement. The reporting requirement, which the government hopes will reduce fraud, took effect Jan. 1 and has been a burden to administer, District officials said. Many of the eliminations occurred when forms were returned incomplete, or not returned at all. Officials claim that many of those eliminated as a result of this requirement have now been reinstated or are awaiting reinstatement.

* Medicaid: The only local impact on Medicaid has resulted directly from the reduction in AFDC recipients, many of whom are automatically disqualified for Medicaid once they lose their AFDC benefits. The number of Medicaid recipients dropped from 107,562 in October, 1981, to 103,273 in April of this year, corresponding approximately to the number of people who lost their AFDC eligibility. Matching federal funds have also been reduced, with every $1 spent by the District being matched by 97 cents from Uncle Sam. This year's Medicaid budget for the District has been set at approximately $200 million.

* Maternal and Child Health grants (MCH): Through community health centers and other medical sources, this program provides a broad spectrum of services from prenatal care to immunizations. D.C.'s share was reduced from $7 million in 1981 to $4.2 million this year. Yet District officials claim the effect will be minimal because of a carry-forward of surplus funds from fiscal 1981. To further cushion the cut, the District has requested a supplemental grant of $945,000.

* Women, Infants and Children (WIC) Program: This program was begun in the District last June and so far has not suffered much from budget reductions. It provides supplemental foods to infants and children determined by a physician to be at risk, and counseling on nutrition to pregnant and nursing women. This program is especially important because of the District's high infant mortality rate. In 1981 the program received a $1.2 million grant, which was increased to $3.5 million this year. The program's rolls have increased steadily from 2,000 in 1981 to about 7,000 this year. D.C. officials estimate that 30,000 people could qualify for the WIC program.

* Food Stamps: There have been major changes in eligibility requirements for this program, which is administered by the U.S. Department of Agriculture. The most significant is that eligibility is now determined on gross rather than net income. Because of this change, food stamp rolls dropped from October to February by 4,968 households. In March, though, the rolls increased by 1,500 households, as some of those dropped from the AFDC program became eligible for food stamps because of their reduced income.

The District government, however, has not turned its back on those suffering from cuts in social services. For example, while federal guidelines eliminated from the AFDC program pregnant women and children between the ages of 18 and 20 currently in school, District officials say they are disregarding the guidelines and including them at a cost of about $1.3 million.

But even with the District's attempts to cushion the impact, the tell-tale signs of desperation are clear throughout the city, with many programs that provide emergency assistance to those critically in need being swamped with requests for help.

Emergency food distribution is one of the areas most visibly affected. Dorothy McKinney, chairman of the Capital Area Food Bank, said the amount of food her agency distributes has risen by almost 30 percent compared with March 1981.

"It is my contention that the administration's proposed cuts in the AFDC and food stamp programs, along with reductions which have occurred to date, have precipitated a hunger crisis here in the nation's capital and throughout the country," McKinney said at congressional hearings about AFDC cuts earlier this year.

The food bank, a private nonprofit corporation, solicits surplus and salvage goods from local and national distributors who receive a tax write-off for their contributions. The food is distributed to approximately 160 nonprofit organizations that serve about 50,000 needy persons a month in the metropolitan area. Since the food bank opened in April, 1981, well over 1.5 million pounds of food have been distributed, McKinney said.

Bread for the City, one of the nonprofit food pantries which distribute canned goods, bread and cheese to needy people in the District, used to serve an average of 500 people a month, said Bread volunteer Lisa Klein. Since October, that figure has jumped to 800.

"I used to be able to take lunch, but now I'm so busy I can't anymore," Klein said.

The type of clients patronizing Bread for the City and other agencies is also changing as the recession cuts across a broader social range.

"Our clients are starting to get better dressed," said Klein. "It seems that more and more people are falling below the poverty line."

"It's not the traditional core [of poor] anymore -- the typical single woman on public assistance," she said. Many of those now seeking help, Klein said, are men, especially those who have lost jobs recently and need food for their families, and those who have suffered cuts in food stamps.

Klein said the food pantry is overspending its budget and will have to increase it by almost half this year to provide the same services. "We're very concerned as the clients keep increasing. Miracles do happen, and what we've been relying on a lot lately is miracles."

According to Nancy Amidei, director of the Food Research and Action Center (FRAC), a Washington-based public interest law firm, unemployed families or families without food stamps turn first for help to the emergency food systems. "I think that the emergency food systems represent an early warning system that something is going wrong. People are not able to feed themselves and provide for themselves."

Officials of social service agencies in the District that provide emergency assistance, shelter and counseling say they are being taxed far beyond their capabilites.

"We are getting more referrals now than ever before," aid Marita Dean, supervisor of the financial assistance program for the Associated Catholic Charities, a social service agency. According to Dean, demand soared at the beginning of winter and has been high ever since. Currently, the agency's case load is 150 percent higher than during the same period last year.

The District has already begun to prepare itself for possible future cuts. According to Julie Rogers, spokewoman for the D.C. City Council's Committee on Human Services, the council has earmarked $250,000 in fiscal 1983 to make up for possible cuts in the Women, Infants Children Program, which may be combined with the Maternal and Child Health program.