The House Ways and Means Committee yesterday approved a bill to sharply curtail most of the tax breaks for leasing property and equipment that were granted in 1981 to corporations and investors.

But an amendment adopted during two days of closed-door negotiations would allow the Navy to proceed with its controversial plan to lease up to 13 cargo ships for the Rapid Deployment Force from private owners.

In marking up the so-called Pickle Bill--named for its chief sponsor, Rep. J. J. Pickle (D-Tex.)--the committee agreed to curb a fast-growing movement by cities, hospitals, colleges and other tax-exempt organizations to participate with private investors in utilizing the tax breaks granted in the Reagan administration's 1981 tax cut.

These organizations, including the Navy, have no need to reduce their taxes. So they were arranging, in growing numbers, to lease buildings and equipment from private owners, who reaped tax breaks from the accelerated depreciation and passed some of the savings on to tax exempt institutions.

As approved by the committee, the depreciation schedules would be stretched out for property acquired in deals such as the one proposed by Bennington College, one of the most expensive private schools in the nation. Bennington was planning to sell its campus to private investors and then lease it back--a transaction that would be made far less attractive by the bill reported out yesterday.

Similar legislation is pending in the Senate Finance Committee.

The Ways and Means bill also would restrict the depreciation tax breaks for property and buildings in which more than 10 percent of the cost is financed by tax-exempt bonds, or for which the term of the lease is for more than 80 percent of the useful life of the property.

In an effort to curb what committee staff members called "double dipping" or even "triple dipping" at the taxpayers' expense, the tax credit granted for rehabiliation of buildings would be cut off for property used by a tax-exempt organization and financed by tax-exempt bonds.

The restrictions would apply to leasing arrangements made after May 23, the date the bill was introduced, but organizations that had "binding contracts" to enter into leases by the end of the year would be permitted to keep their tax breaks.

The Treasury Department endorsed the bill and committee members worked closely with Treasury in marking it up. They agreed to exempt from the bill's restrictions leases of computers, high-technology hospital equipment, and some telecommunications equipment.

James M. Verdier, a senior tax analyst for the Congressional Budget Office, said the potential revenue losses from the existing law are "extremely large.

Government and tax exempt organizations currently own more than $2 trillion in property that could be transferred to private investors and then leased back," as Bennington sought to do.

It was the Bennington plan, along with the proposed transfer of publicly owned sports arenas, city halls, hospitals and other facilities, that generated pressure to close what Pickle called "one of the most unusual, ingenious, and costly tax shelters that we've seen in years."