The numbing, grief-filled day after her brother's death last week was not the best time for Bessie McLean to learn about one of the Reagan administration's budget cuts, the $255 Social Security death benefit that she was counting on to help pay for his burial.

McLean, who earns $14,000 a year as a D.C. government secretary and lives in Hyattsville, was forced to delay paying her own bills this month in order to purchase a $375 grave site for her brother. Because he had lost his job two weeks before his death, he no longer had life insurance, so she will probably have to take out a loan to pay the $895 cost for his funeral.

"It's such a little amount, who says it's all right to drop it?" McLean asks, referring to the Social Security benefit. "It might not matter to rich families, but it does matter to families like us."

McLean's experience is similar to that of an increasing number of poor and working poor families, who because of hard economic times and sharp cutbacks in Social Security and veterans' death benefits, find they cannot afford to bury their dead. Their difficulties have forced funeral directors to offer installment plans and cheaper services, resulted in more cremations and donations of bodies to medical schools and forced local governments, churches and charities to assume a greater role in paying funeral costs and supplying burial plots.

The reduction in Social Security and veterans benefits was an attempt by the Reagan administration to cut down on payments that anyone who has life insurance -- and 4 out of 5 American families have such policies -- receive anyway. Until last fall, anyone on Social Security rolls automatically received a $255 lump sum payment for funeral expenses. Under the new regulations, only those with surviving spouses or dependent children receive any money. About 700,000 people are affected by the Social Security cuts.

Veterans with honorable discharges used to receive $300 for a funeral and $150 for a cemetery burial from the Veterans Administration. The new regulations preserved the $150 payment, but dropped the funeral expenses except for those who died in a VA hospital or who receive VA pensions.

Administration officials estimate that $285 million was saved in the first year alone by the reductions, and contend this represents a Reaganomics success story because payments were stopped to thousands of people who did not need them. The cuts provided no safety net for the poor and working poor without insurance at a time when the average cost for a funeral, not including casket, headstone or grave, is $1,980.

"The old people have always had little $500 or $1,000 burial insurance policies and they're counting on the Social Security to be added," said Frances Mason Jones, owner of the Mason Funeral Home in Southeast Washington. "I have to tell them when they call and many people just plain don't believe me."

Local funeral directors say that many families, even those who meet the strict guidelines for welfare funerals offered by state and local governments, are going into debt for their relatives' funerals rather than turn to charity burials.

"It's putting a lot of pressure on families," said Rupert Baker, a funeral director at Chinn's Funeral Home in Arlington, which handles the majority of the county's welfare funerals. Baker said that in the last year there has been a 20 percent increase in the number of clients without any means of paying for a funeral. "They're paying us in installments, some as little as $12 a month." In some cases, services have been delayed for up to four days until a family could raise the cash necessary for a grave, Baker said.

The increasing cost of Baltimore grave sites prompted 62 funeral directors to buy two abandoned cemeteries in order to keep supplying low-cost funerals to private customers and charity funerals to the city and state, which by law cannot exceed $400.

"Cemeteries have stopped accepting charity bodies," said George Gonce, a Baltimore funeral director and secretary of the state mortician's board. "These cemeteries charge $250 and the average cost of a plot is $450 at a commercial cemetery. In rural areas, you get church cemeteries that will assist, but a lot of these people are unchurched."

In Arlington, the congregations of the Mount Olive and Mount Zion Baptist churches have been asked from the pulpit several times this year to donate money for the funerals of impoverished neighbors, according to John Robinson, director of the Martin Luther King Center, a private social agency in the city which has received a growing number of requests to help pay for funerals.

The District of Columbia, Virginia and Maryland all provide funds for indigent funerals, but many of the working poor are not eligible for them. Officials in the District of Columbia, which pays $801 for an adult funeral, Maryland, where there is a $400 maximum, and Virginia, which pays $500, describe various income requirements as "strict" and not well-publicized.

The D.C. Dept. of Social Services paid for 649 funerals in 1981 at a cost of $447,435. Although final figures are not yet available for this year, Norman Bush, director of indigent burials for the city, said he expects the weak economy to increase applications. Funeral directors in the city, like Don Ellis, manager of Dudley's Funeral Home, say they have handled 10 to 15 percent more welfare, or "city" funerals in the last year.

"With so many people laid off and the economy so bad, people just can't afford funerals," said Ellis. "There are more than usual using the service."

Fairfax County operates a cemetery for indigents and will pay up to $900 for other funeral expenses.The county has experienced a slight increase in charity funerals since the federal benefits were dropped, with 32 burials so far this year, compared to 27 in 1981, but a spokesman for the county's Department of Social Services said it is too early to determine the exact reason.

Local governments in this area and over the country are expanding their roles in the funeral business, to pay for funeral costs once covered by federal programs and to deal with increased requests for help.

"The families are going to the county boards of supervisors requesting any kind of aid," said Mark Forberg, secretary of the Virginia state funeral board.

In Los Angeles, the county supervisors last month authorized $10,000 to pay for charity funerals because of the growing number of unclaimed bodies of veterans in the county morgue.

Since the veteran's benefit was dropped, 44 unclaimed bodies of veterans have become, by default, the responsibility of Los Angeles County, according to Robert Kingsbury, director of military affairs for the county. "The county picked it up out of the goodness of their hearts," he said. A $9,000 donation by a Vietnam-era veteran has helped, but the county predicts it will be forced to continue paying for funerals.

VA officials told a Senate committee that the bodies of only 256 veterans could not be buried since the funeral benefit ended Oct. 1 and only 115 would have been eligible for the now-ended benefit. The agency's position is that the cuts have caused problems only in isolated cases.

"The whole emphasis is on volunteerism and getting the local community to take care of its own," said Charles Lucas, a VA spokesman.

Americans' increasing transience and family disintegregation has meant there hasn't always been a local community to help. The membership of the Veterans of Foreign Wars, angry that local posts have been forced in the last year to pass the hat to pay for some veterans funerals and angry that a promised benefit was erased, has asked the Veterans Administration to take care of funerals for indigent veterans.

A bill to allow VA to pay for indigents' funerals has passed the House and is pending in the Senate, but would affect relatively few veterans.

Meanwhile, Tom Nelson, of the American Association of Retired Persons, has found a new nervousness about death costs among the groups he counsels on funeral planning. "There's a tremendous number of people who are not indigent and to whom these (government) benefits were very important. There's more concern about how people are going to pay for their burials."

In some cases, the problem is avoided. A slight increase in the number of bodies donated to science has been noted by anatomy boards in Maryland and Virginia. Donated bodies are cremated free within two years, and the ashes are returned to the family. Dr. George Goode, chief of the anatomy department of the Eastern Virginia Medical College in Norfolk, which is one of three schools in Virginia participating in the body donation program, noted, "Donations have increased, mostly because of funeral costs. Although people don't have to give us a reason, the expense to others and the economy is often mentioned."

Cremations, which usually cost less than $500, also are increasing. The method is used now in 10.9 percent of all deaths, up from 9.7 percent in 1980 and 9.4 percent in 1979. "Some families are going more for cremation, simply to save several hundred dollars," said Ed Weber, a Baltimore funeral director.