As Congress prepares to adjourn without passing new banking legislation, it will leave more than 350 financial institutions lined up to climb through loopholes in the present law.

How federal regulators handle the nonbank bank issue could have an significant impact on the future direction of the banking industry.

Comptroller of the CurrencyC. T. Conover, who has said he will have no choice but to let banks use the loopholes unless Congress closes them, is expected to issue a statement after Congress quits saying he plans to begin processing the applications. The first approvals could come in a few weeks.

The biggest loophole is one in the federal Bank Holding Company Act that allows bank holding companies to expand nationwide in defiance of a federal law that prohibits interstate banking, by establishing so-called nonbank banks.

Also called consumer banks, limited-purpose banks or loophole banks, they are institutions that do not meet the strict definition of a bank under the bank holding company law. The law says a bank is a business that both takes demand deposits (checking accounts) and makes commercial loans. By dropping one or the other, the company is not bound by the geographic limitations imposed by Congress.

The comptroller faces the largest backlog of applications with 329. The Federal Deposit Insurance Corp. has 20, and the Federal Reserve is sitting on two.

The Independent Bankers Association of America has appealed to the White House to stop the spread of these institutions. They are also bitterly opposed by the Federal Reserve.

In most important respects, a nonbank bank resembles any other bank. Its deposits are federally insured by the Federal Deposit Insurance Corp. and it is subject to the same federal examinations for safety and soundness.

No nonbank banks have failed, but if they do, it will be handled like any other bank failure by regulators.

In March of this year, the Federal Reserve counted 61 nonbank banks that had been established, most of them in the last two years. About half of them are owned by securities firms, such as E. F. Hutton, Merrill Lynch, Prudential-Bache, and Drexel Burnham Lambert. The others are owned by insurance companies, financial services organizations, and industrial and retail companies, including Chrysler Corp., Gulf & Western, Control Data Corp., J. C. Penney, Parker Pen Co., and McMahon Valley Stores, a California furniture chain.

Conover declared a moratorium on approving new nonbank banks in April 1983. When that limit expired a year later, he approved eight more and then reimposed the ban until the end of the congressional session.

The FDIC has approved 68 applications since 1968, all but seven of them in 1983-84. Unlike the comptroller's office, the FDIC never imposed a ban, taking the position that there was no legal reason for refusing to act on applications.

The rush started last spring when the Fed reluctantly approved the application of U.S. Trust Co. for a nonbank bank. Since then, 46 bank holding companies have applied to set up 329 nonbank banks around the country. The biggest single request comes from Dimension Corp., which has aims to set up 31 offices in 25 states; four of those branches have already been granted, including one in McLean. The FDIC's applications are from companies like Merrill Lynch, Teledyne, Bear Stearns, and ITT Financial Corp.

In this area, applicants to form nonbank banks include American Security Corp., Washington Bancorp, First Maryland Bancorp, Suburban Bancorp, Equitable Bancorp and Maryland National Corp. In addition, money center banks like Citicorp and Mellon National Bank have filed to start nonbanks in metropolitan Washington.

The Senate and House banking chairmen, who failed to get loophole-closing legislation passed, have said that they would try to make any future bill retroactive to July 1983. Their provision would require any nonbank banks approved in the interim to divest their interstate operations.

The second loophole left unclosed by the legislators is known as the South Dakota loophole. It is so named because it allows banks to offer otherwise prohibited services like insurance. A South Dakota law enables a state-chartered bank to sell insurance in every other state so long as the bank does not do so within state borders. Citicorp, which took its credit card operations to South Dakota to evade New York's interest rate ceilings, has bought a state-chartered bank there in hopes of going into insurance.

Citicorp's application is still pending at the Federal Reserve "until Congress acts," a spokesman said yesterday. The Fed has also given the same treatment to a similar request by Bank of America.