Prince William County should push builders and developers to construct more affordable housing, a county housing task force said in a recently released report.

The report was ordered after Tropical Storm Lee flooded Holly Acres Mobile Home Park in Woodbridge last year. Many of its low-income tenants were left searching for a place to live, and county activists noted the dearth of low-income housing available to them.

The report found that of the county’s 137,115 housing units, 0.8 percent are mobile homes, 57 percent are single-family houses, 26 percent are townhouses and about 16 percent are multifamily units, including apartments.

The housing task force that led the study found that Prince William has made strides since initial studies were completed, in 1989 and 2005, including encouraging the development of affordable housing in long-range planning documents and providing financial support to community nonprofit groups that help provide affordable housing.

Those efforts, however, are voluntary and change year to year. Elijah Johnson, housing and community development director, told the Board of County Supervisors that Prince William could mandate more affordable housing by passing an ordinance to deal with the issue and setting goals each year to build a certain number of units.

County officials noted, however, that Fairfax County and other Northern Virginia localities tend to have far fewer lower-priced housing than Prince William.

According to the report, the county lacks 8,220 units for people who make up to 30 percent of the area’s median income, or up to about $28,000 annually. Affordable rent is considered to be $483 monthly.

Finding housing for those residents is a perennial, difficult issue, Johnson told supervisors.

“Finding solutions for them is going to take some time, and we’re going to have to rely on our federal and state partners,” Johnson said.

The struggle to find housing also exists for those at the top of the economic spectrum. According to the report, there’s a deficit of as many as 24,604 units for people making more than $112,000. Those in that income can afford monthly rent of $2,567.

Supervisor W.S. Covington III (R-Brentsville), whose fast-growing district has large tracts available for development, said there would be little appetite from him and possibly the rest of the board for the types of reforms recommended in the housing report.

Covington said that many localities encourage affordable housing by allowing developers to build projects with more density in return for more affordable units.

But with issues such as congested roads and crowded schools, Covington said, some residents or supervisors might be hesitant to support such an ordinance.

“I can’t tell you that people are completely against it, but they don’t want to go back to the days of not being able to move” in traffic, he said. “You can’t absorb those masses of people.”