The District of Columbia commission charged with policing the city's 10,000 physicians has taken formal action on only one case in the past three years and has a backlog of 174 complaints of illegal or unethical activities, officials of the Commission on Healing Arts said yesterday.

During continuing hearings on the city's fiscal 1984 budget in the House Appropriations subcommittee on the District, commission staff director P. Joseph Sarnella said the five staff members on the commission are not enough to handle the caseload.

"We have cases where physicians have written millions of dollars of illegal prescriptions , and they the doctors are still out there," said Dr. Alyce Gullattee, president of the commission and also head of the city's Alcohol and Drug Abuse Services Administration.

In one case, a doctor was first convicted 3 1/2 years ago and again two years ago of selling prescriptions for excessive amounts of controlled substances. One way drug abusers get drugs is through such prescriptions.

That doctor is still licensed to practice medicine in the District because of the inadequate staffing on the commission and the long formal process required before a license can be revoked, Gullattee said in an interview.

"You feel virtually impotent to do what has to be done," she said. "People say we are not policing them, that we are just giving them a slap on the wrist."

Last year, the appropriations subcommittee increased funding for the commission to bring its fiscal 1983 budget to $400,000 and 12 staff positions. But Sarnella testified that the commission never got the added funds, and that its actual fiscal 1983 budget was $277,000, with only five staff positions filled now.

Subcommittee Chairman Rep. Julian C. Dixon (D-Calif.), in one of his strongest statements of intent during these hearings, said his panel will add funds to the commission's budget again this year. He closely questioned the mayor's budget representative, Wilhelmina Marshall, on why the funds Congress put in last year were not used for the commission. "This is very serious, in my opinion," Dixon told Marshall.

Marshall replied that while the city is "sympathetic with the committee's recommendation," it had to look at the overall budget constraints, she said.

"It was stronger than a recommendation," Dixon replied. "I think we will do the same thing this year, and I will talk to the [mayor's] budget office about it."