At least eight top officials of the Health and Human Services Department may be holding their jobs illegally because the White House has failed to send nominations to Congress, Sen. William Proxmire (D-Wis.) charged yesterday.

Proxmire said a Congressional Research Service study had concluded that, under 1966 provisions of the Vacancy Act, agencies are prohibited from using a temporary or "acting" officeholder for more than 30 days to fill jobs that are subject to Senate confirmation.

Several top HHS jobs, he said, have been filled on an acting basis for more than a year. Nine of the 17 HHS positions requiring Senate confirmation are vacant or filled by persons on an "acting" basis.

Proxmire called it a "sorry state of affairs" caused by the "continuing feud between the White House staff" and Secretary Margaret M. Heckler over nominees. He said he is "concerned that the functioning of the agency" is being "crippled by a myriad of acting officeholders."

"We have a government to run. And this isn't the way to do it," Proxmire said. He added that he will ask the comptroller general of the United States "for a definitive ruling on the legality of this practice" and for a study of how prevalent it is in other agencies.

HHS press officer Claire del Real said the department is following the same practices as all other agencies. "We believe that all HHS officials carrying out the secretary's duties are legally holding their jobs." She cited the plan that created the Health, Education and Welfare Department in 1953, which she said authorizes the secretary to delegate responsibilities. "Since the designation of these employes is not made under the Vacancy Act," Del Real said, "the 30-day limitation does not apply."

A survey yesterday by The Washington Post of the Agriculture, Interior, Commerce, Housing and Urban Development, Labor, Transportation, Education and Justice departments found 30 jobs that are subject to Senate confirmation that were vacant or filled by an "acting" appointee, in some cases for many months. Only 11 nominations for the jobs have gone to the Senate.

The president's failure to fill key HHS positions has been a sore point for a year or more. There has been speculation that some of Heckler's choices are too liberal for White House staffers, while others suggest that conservatives in the White House are trying to frustrate Heckler to the point where she resigns.

At HHS, the undersecretary job has been vacant since the summer and there is no nominee. In addition, James O. Mason has been acting assistant secretary for health since January; Robert Helms has been acting assistant secretary for planning and evaluation since April 1984; Carol Fraser-Fisk has been acting commissioner on aging since the start of this year; Martha A. McSteen has been acting Social Security commissioner for two years; Lawrence De Nardis has been acting assistant secretary for legislation for about a year; C. McClain Haddow has been acting administrator of the Health Care Financing Administration since Aug. 9, and Bryan Mitchell has, in effect, been acting deputy inspector general for about four years.