The chairman of the Securities and Exchange Commission yesterday said the accounting profession should be given a year to show that it can police its own operations before Congress decides whether broad federal controls of accountants are necessary.

Appearing as the final witness of a long series of hearings on accounting before a Government Operations Subcommittee, chairman Harold M. Williams called on the industry "to initiate positive and effective action" by July 1, 1978.

Williams said that the SEC could issue annual reports, beginning next year, "on our progress and that of the profession" in responding to recent criticism.

The hearings grew out of a broadly critical report by the subcommittee staff called "The Accounting Establishment" and published last January.

The report, which concentrated on the Big Eight firms, said auditors have become advocates of "the self interests of their corporate clients." It also knocked the SEC of not monitoring the way publicly owned companies are audited.

"The most important requirement of independent auditors is that they be regarded by the public as truly independent," the report said. But it concluded that Big Eight firms had "seriously impaired their independence" by providing clients with such services as consulting and executive recruitment."

During the hearings, each of the Big Eight firms testified or submitted statements. Their opinions ranged from Peat, Marwick, Mitchell & Co., which came out strongly for continued self-regulation by the profession, to Price Waterhouse & Co., whose senior partner shocked many of his fellow accountants by proposing federal registration of accountants to restore public confidence.

Williams testified that "one of the most important approaches to the strengthening of auditor independence lies in the formation of audit committees composed of independent corporate directors."

The New York Stock Exchange has adopted rules calling for member corporations to have independent audit committees.

He said that the SEC "has already acted to discourage reporting companies from using the power to discharge auditors as a means of undermining auditor independence."

The SEC intends to consider whether a corporation should detail in its proxy statements "all services which its independent accountant performs, together with a listing of the fees" paid for those services, Williams said.

A staff member of the subcommittee - which is headed by Sen. Lee Metcalf (D-Mont.) - said "we're going to know by Halloween" whether the accounting profession will reform itself or federal regulation will be necessary. The American Institute of Certified Public Accountants - the biggest professional association of CPAs - holds its annual meeting in October.