REAL PROGRESS is finally being made toward giving citizens some defense against official snooping into their bank and credit-card accounts. As part of its omnibus bank-regulation bill, the House Banking Committee has just approved provisions that would ensure individuals notice of, and a chance to challenge, most government demands for financial institutions' files on their accounts.

Congressional action is needed because the Supreme Court has taken such a crabbed view of the privacy interests of bank customers. In 1976, the court held that the information in the bank's custody is the bank's property; the customer has no privacy claims and no right to intervene if a government agency tries to rummage in those files. That make financial privacy something of a joke.

The House bill shows a much better grasp of economic realities. It also reflects a commendable change in the attitudes of federal law-enforcement agencies. Until recently they opposed all such legislation on the grounds that white-collar criminals and others might use it to frustrate legitimate investigations. But contrary to many prosecutors' predictions, the notice-and-challenge rules that Congress imposed on the Internal Revenue Service in 1976 have not seriously hurt enforcement of the tax laws. Individuals have challenged only about 3 percent of the thousands of summonses issued by IRS since that law took effect. The agency has won every test taken to court. Although the statute may need some refinement, this experience does show that a carefully drafted general law can accommodate both privacy protections and law-enforcement needs.

The administration is still wary. That is evident in the Banking Committee bill, which is largely a compromise worked out by administration lawyers and a House group spurred by freshman Rep. John J. Cavanaugh (D-Neb.).Compared with earlier proposals, the committee measure generally gives federal investigators more flexibility and requires a citizen to take more legal steps in a shorter time to keep his challenge to a subpoena or summons alive.

Many of those changes are sound. Two are not. Of those, one would grant the Securities and Exchange Commission special authority to notify customers of subpoenas a few days after, not before, the records have been obtained. The second would exempt grand jury subpoenas almost entirely.

Still, the committee measure is a good start. It should stimulate action in the Senate, where Alan Cranston (D-Cal.) and others have already explored the issue extensively. Moreover, the bank-regulation bill is a vehicle with considerable momentum. All in all, this could be the Congress that finally brings financial-records law more into line with most citizens' concepts of fair play and privacy.