The Fairfax County Board of Supervisors, responding to police charges of widespread illicit sexual activity at all eight of the county's massage parlors, yesterday ordered a public hearing on a proposal that would effectively ban the establishments as they now exist.

A hearing was set for Jan. 16 on a proposed amendment to the county's massage parlor ordinance that would prohibit male-female massages.

The Alexandria City Council last week severely restricted the operation of massage parlors in that city. Referring to that action, Fairfax board chairman John F. Herrity yesterday told his fellow supervisors, "I just want to make sure [the Alexandria operators] don't come over here and get established."

The vote was unanimous, with Supervisor Martha V. Pennino (D-Centreville) absent.

The cross-sex massage ban has been strongly backed by police officers who say that massage parlor employes have learned techniques that, in the words of Fairfax police chief Col. Richard A. King, "would require the policeman to compromise himself" in order to make an arrest for prostitution.

"I would not allow that sort of thing. It is contrary to law," King said in an interview yesterday.

As a result, only three arrests for prostitution were made at massage parlors this year although "practically all of the county's 200 licensed massage technicians are engaged in illegal sexual conduct," according to a police report presented yesterday to the supervisors.

A massage parlor manager, Charles Coughlin of Valentine's Health Club, 8503 Lee Hwy., disputed the police statement in an interview last weekend. Coughlin said the club's 20 women employes are required to take regular polygraph tests to assure that illicit activity does not take place.

Hui Lee, owner of the six-employe Geisha House at 7031 richmond Hwy., also denied that sexual activity occurs at her establishment and said massages involving members of the same sex would be "not natural."

"I do not know what the American social system is coming to," she said.

Under the current ordinance, massages may be administered only by licensed technicians in county-regulated establishments. Neither employes nor customers may "touch. . . fondle. . . or massage" the erogenous area of the other party.

"Police said yesterday that since the adoption of the county's massage ordinance in January 1976, an unspecified number of undercover officers have been assigned to the establishments. King refused to say exactly how many officers were involved in the undercovery operation.