The Department of Housing and Urban Development announced yesterday its first new housing program since President Reagan took office--an information service to help local governments help each other lower housing costs.

In line with the administration's emphasis on deregulation and budget savings, the demonstration program will cost less than $1 million a year and has a Cheshire-cat-smile quality about it: the better it works, the more the government disappears.

HUD will act mainly as a clearinghouse for ideas generated at the local level for reducing building-code requirements and relaxing zoning restrictions. It will encourage builders and city officials to work together, and will provide each city with an information packet of 10 different HUD pamphlets.

The lack of federal grants or recommendations suits the local governments just fine, said Joseph Sherman, director of HUD's division of construction technology, describing what happened when they were asked to participate.

"When we made the calls, the universal reaction was, 'Well, what do we need the feds for?' We said, 'You don't.' When we said that, they were all interested," Sherman said.

HUD Secretary Samuel R. Pierce Jr., announcing the new program, pointed out that 90 percent of persons who rent cannot afford to buy a home because of high costs. While the problem primarily involves high interest rates now, Pierce said home prices can be reduced as much as 20 to 30 percent by cutting local regulations.

The project--called the Joint Venture for Affordable Housing --will involve local builders and community groups as well as such national groups as the National Association of Home Builders, the National Association of Counties, the International City Management Association and the Council of State Community Affairs Agencies.

Representatives of these groups, as well as of the National League of Cities and Conference of Mayors, were on hand for a joint press conference at HUD yesterday to hail the program while recognizing its limited nature.

"Mainly we're talking about a change of attitude," said NACo Executive Director Bernard Hillenbrand. "Up until now we have had to face hostility" from the federal government. Asked if his group was disappointed that no federal grants were involved, Hillenbrand said, "There's not going to be any federal money for anything, except building bombs or something."

The demonstration project will begin in 11 communities: Ann Arbor, Mich., Coral Springs (and Broward County), Fla., Birmingham, Lincoln, Neb., Manchester, N.H., Phoenix, Riverside, Calif., San Diego, Tulsa, Wichita, and Everett, Wash.

Another four are to be selected from 350 around the country that have applied so far, HUD officials said.

Builders' problems with local regulations are exemplified by plastic bathtubs in Rockville, said W. Evans Buchanan, past president of the NAHB. So many local officials had to approve the use of the less costly material, he said, that it added unnecessary delays--and therefore expenses--to building homes there.

HUD officials also said local rules to restrict population density drive up the cost of building homes. HUD Undersecretary Donald Hovde said the country "has developed the attitude that higher density is bad" for the environment and for urban planning, "but it's not true. I don't know where that came from."