Washington and its suburbs face a severe shortage of inexpensive housing that threatens to drive low- and moderate-income workers away from the area, the Metropolitan Washington Council of Governments warned yesterday.

One in eight households in the metropolitan area needs government assistance to find adequate housing because of financial problems, an oversupply of run-down dwellings and the severe shortage of affordable housing, a study released yesterday said.

In a news conference, local officials struck a pessimistic tone, predicting that low- and moderate-income workers, including municipal employes and teachers, will be forced to reside outside the area unless more inexpensive housing is made available.

"Unless something substantial is done, this Washington area is going to become virtually exclusively the home of two-income and relatively high-income individuals," said Alexandria Mayor James P. Moran Jr. "We will lose . . . the diversity we're all so proud of."

Both Moran and Jo Ann T. Bell, a member of the Prince George's County Council, sidestepped questions about what specific steps might be taken to provide more affordable housing.

Asked if the situation could be characterized as desperate, Moran responded: "That's intended . . . . There is no real solution."

Bell, citing the COG's finding that 134,135 households in the region need housing assistance and another 33,619 households are on local waiting lists for low-income housing, said, "If we heard this about the people of a Third World country, we would be concerned. To know that this is true in our nation's capital is nothing short of shocking."

Among the major findings of the COG study:

*The number of applicants in the area on local waiting lists for low-income housing more than doubled in the decade preceding 1984, growing to 33,619 from 16,022.

In Fairfax County alone, the figure leaped to 2,900 from 352, an increase of 724 percent. In Montgomery County, the figure tripled in the decade.

*A large and growing number of low-income households are paying more than a third of their income for housing costs.

Those with the lowest incomes are paying the greatest portions in rents.

*Federal subsidies for most rental housing, already sharply curtailed by the Reagan administration, will expire in the next decade, squeezing local governments seeking low-income housing options even further.

*The shortage of affordable housing is compounded by the growing number of low-income, single-parent households in the region, about 85 percent of which are headed by women, as well as by the fast-growing number of elderly in the population, nearly half of whom have annual incomes of less than $15,000.

The study goes to the COG Board of Directors for consideration at its July 10 meeting.

Both Bell and Moran urged the federal government to shoulder more of the burden of providing assistance to low- and moderate-income housing-seekers, and stressed that local governments are ill-equipped to subsidize housing themselves. "We just can't meet that need," said Moran.

As an example of the shrinking availability of inexpensive rental units and the displacement of low-income tenants, Moran pointed to Alexandria's Abingdon Apartments.

The 242-unit complex was one of the city's last inexpensive residences until it was bought by a developer who plans to remodel it. City officials say virtually all the apartment's tenants will be forced out of the building in the next four months as one-bedroom monthly rents of $340 jump by more than $200.

Both Moran and Bell mentioned in passing the need for cooperation between local governments and the private sector to provide more inexpensive housing, but neither would venture a particular proposal. Asked about incentives for developers to provide low- and moderate-income housing, Moran said, "The largest incentive is a moral one."

In Fairfax County, politicians and civic leaders have called for public-private partnerships to address the problem, warning that businesses considering the area will not come to the region if their workers cannot find adequate, affordable housing.