The House Banking Committee passed and sent to the floor yesterday a bill authorizing financial institutions across the country to pay interest on checking accounts. The legislation, which has 251 cosponsors, is expected to pass next week. A similar measure will be considered by a Senate committee next Wednesday.

The bill also authorizes the automatic transfer of funds from savings to checking accounts in banks, the establishment of remote service units by federally chartered savings and loan associations, and share-draft accounts by federally insured credit unions. Remote service units transfer funds from a customer's savings account to a third party's account, such as a store, at the point of sale. Share drafts function like checks.

The legislation was made necessary when the U.S. Court of Appeals ruled last April that these devices violated prohibitions against paying interest on checking accounts, despite the approval of federal regulatory agencies, and had to stop Jan. 1.

As a consequence, competing types of financial institutions were suing each other, claiming that their rivals were acting illegally. The court invited Congress to settle the issue by amending the Federal Reserve Act to legalize the new types of transactions. By the time the House took action, between 3.5 million and 4 million Americans had deposited some $10 billion in the various accounts.

The House version would authorize banks and thrifts nationwide to open NOW accounts for individuals and non-profit organizations effective Sept. 30, 1980. A NOW, (negotiable order of withdrawal) account allows a saver to write a check-like draft on his or her savings account. Such accounts currently are permitted only in New England and New York. In these states, some 68 percent of the commercial and savings banks and the savings and loans offer NOW accounts. The 2.7 million existing accounts have balances totaling $5.9 million, according to the Federal Reserve Banks of New York and Boston.

Consumer groups championed NOW accounts but many in the savings industry opposed them due to increased costs. Rep. Frank Annunzio (D-Ill.) has been a persistant critic of NOW accounts on the grounds that they will do nothing for small savers and actually hurt them.

He introduced an amendment at yesterday's mark-up session requiring banks to pay interest on accounts with as little as $100 on deposit. In fact many banks require much higher minimums; Citibank's, for example, is $3,000. Annunzio's motion was defeated, 22 to 9. The committee then went on to pass the bill by 35 to 4.

The Senate version legalizing NOW accounts also calls for removal of state usury ceilings and Regulation Q, which sets a limit on interest rates financial institutions can pay and guarantees that savings and loan associations can pay one-quarter percent more interest than banks.The American Bankers Association, which wants to get Regulation Q lifted, tried unsuccessfully yesterday to get an amendment to that effect introduced. According to staffers, such a move would have seriously compromised the bill's possiblity of passage.

The National Association of Mutual Savings Banks -- many of whose members currently offer NOW accounts -- hailed the committee vote.

"The overwhelming vote indicates broad consumer acceptance, and we only hope the Senate will follow suit," the bankers said. "NAMSB is also gratified that the House banking leadership considered this important matter independently of Regulation Q issues."

The Carter administration has indicated strong support for phasing out interest ceilings and the differential paid by thrifts over 10 years. The savings industry says that, whereas it might go along with a phase-out of ceilings, it wants to maintain the differential at least until thrifts are fully competitive with banks in getting new sources of funds other than customer deposits.