Dreyfus Corp., moving quickly to take advantage of its acquisition of a New Jersey bank, is planning to offer cut-rate consumer loans and mortgages, the chairman of the mutual fund company said today.

The decision to move forward into broad scale consumer lending follows a test marketing program of automobile buyers performed six weeks ago at Lincoln State Bank in East Orange, N.J., a small bank Dreyfus bought in October. "It was a very narrow test, but we were encouraged and now we're moving forward," said Howard Stein, Dreyfus' chairman.

Furthermore, Stein said Dreyfus plans to change the name of the bank next week to Dreyfus Consumers Bank as part of an effort to broaden its appeal to a potential national audience.

The moves come in the midst of a continuing bureaucratic war in Washington over Dreyfus' $2.7 million purchase of the small bank. The Federal Reserve Board has objected to the Dreyfus purchase on the grounds that non-banking companies should be separate from banks. But the Federal Deposit Insurance Corp. has given its approval and says the Fed has no jurisdiction over the matter.

In the meantime, however, Dreyfus, which manages a variety of funds, including the money market fund Dreyfus Liquid Assets, is moving ahead with activities that are, to a certain extent, bank-like. Because Stein says Dreyfus, with only 540 employes, can operate with narrower spreads -- the gap between the rate at which banks lend and borrow their funds -- he believes their lending rates can be considerably below those of major commercial banks.

There has been considerable criticism of bankers from top Reagan administration officials, such as Council of Economic Advisers Chairman Martin S. Feldstein, who say high consumer loan and credit card borrowing rates at major banks are far too high.

Stein would not say specifically what interest rate the Dreyfus operation would charge when the program is launched within the next month. The test program, however, offered 11 percent automobile loans to both Dreyfus shareholders and existing bank customers who were also buyers of Fords or Chryslers. This 11 percent rate is nine-tenths of a point less than the automakers' rate and several points below the rates offered by banks.

The sales literature of the program actively exploited the gap between the Dreyfus offer and commercial banks. "It is high time that something was done to bring down the cost of consumer credit," Dreyfus claimed in a letter to shareholders.

Stein said the program means that Dreyfus is "entering a new phase of banking," although there are no current plans to expand the bank beyond New Jersey. Dreyfus has received permission from the Comptroller of the Currency to set up a new national, Dreyfus National Bank & Trust Co., which is not yet operational.