The D.C. Council, bowing to intense public pressure, reversed itself yesterday and killed an estate tax bill that would have raised the cost of inheriting property in the city by about 40 percent.

The council, on a unanimous voice vote with no stated opposition, officially sent the bill back to a committee for futher study, but committee Chairman John A. Wilson (D-Ward 2) said the tax proposal is dead.

"It will just die in committee," said Wilson, chairman of the Finance and Revenue Committee. We'll just go back to the old inheritance tax.

The now-defeated estate tax, approved June 2, would have sharply raised, the levies on inheritances in the District of Columbia, to the extent that they would have far exceeded taxes on estates worth the same amount in Maryland and Virginia. Critics of the D.C. tax, including homeowners and estate lawyers, all argued that the increased taxes here would spur middle-class residents to move out of the city.

Under the defeated tax, a person with a taxable estate of $200,000 after deductions, with no surviving spouse and one who leaves the estate to his children, would have paid $17,500 in District taxes. In Virginia, the same estate would be taxed $1,200, and in Maryland, $1,800.

There is no estate tax in the District. Under the current city inheritance tax, an estate is not taxed until after it has been divided among the heirs and they would pay individual taxes. The proceeds from like insurance policies are not taxed and adult children can now inherit $5,000 tax free. Under the estate tax, insurance policies with named beneficiaries -- now not considered part of a taxable estate -- would have been subject to a tax.

Before the reversal vote, Wilson chastised his colleagues for reconsidering the measure, although he later joined them insending the bill back to his committee.

"The public had a chance to comment on this bill since 1979," Wilson said. "If you want to reconsider it, give the honest reason -- because the tax rate is too high for some middle--class people. The problem is that certain citizens in certain wards of the city don't want to pay the tax. I donht expect any of you to put your political careers on the line, so go ahead and vote for reconsideration."

The council's reversal of its 12-to-1 vote to approve the tax was considered extraordinary since the bill was already in Mayor Marion Barry's hands, awaiting his signature. But since the bill had not been signed, the council invoked one of its rules that allows it to reconsider any bill until the mayor actually takes action.

Barry's lawyers in the Corporation Counsel's office said the council's action was legal and City Administrator Elijah B. Rogers agreed.

"Given the climate and given the council's action, I believe the mayor will follow the council's concerns," Rogers said, adding that the mayor could still veto the bill if the council's action were judged illegal.

Among other things, the tax proposal, revived by Wilson this year, would have made the District's estate tax conform in many ways with the federal estate tax law and thus reduce the number of auditors needed in the city's Finance and Revenue Department. The estate taxes would have raised $1 million in the year starting Oct. 1 and added another $4 million to the 1983 fiscal year budget. The repeal of the tax thus leaves the city with another hole in a budget that is supposed to be balanced.

Council Chairman Arrington L. Dixon said after the vote that the lost money could eventually be recouped by slightly raising the existing inheritance tax.

In other action yesterday, the council on a voice vote raised student bus fare from the current 10 cents to 15 cents and to 20 cents in January. In addition, the council voted unanimously to force banks holding city deposits to release a detailed neighbornood-by-neighborhood breakdown of all their home mortgage and rehabilitation loans, to make sure there is no discrimination -- or "redlining" -- against lower-income applicants from poorer sections of the city.

Council member Polly Shackleton (D-Ward 3) -- whose ward west of Rock Creek Park contains the city's most expensive property and would be hardest hit under the estate tax -- moved that the estate tax be reconsidered.

The council's attorney, Lawrence Mirel, had decided late Monday that the council had the power to reconsider any bill up until the time the mayor signed or vetoed it.

Shackleton, one of the 12 council members to vote for the bill two weeks ago, said she wanted it reconsidered "because the council had no opportunity to hear public reaction to the proposal."

The council scheduled public hearings on a similar estate tax bill last year, but no witnesses appeared. There were no public hearings held since the bill was reintroduced during this council session, which began in January.

Council members essentially had agreed to reconsider the estate tax and then send it back to committee during private meetings and negotiations in the 24 hours before yesterday's meeting. But before the actual vote to confirm what everyone in the packed council chambers already expected, Wilson admonished his colleagues for not admitting that public pressure had forced them to reconsider the tax.

Wilson and Council member Betty Ann Akne (D-At Large), the only council member who originally opposed the tax, engaged in some sharp verbal sparring over the tax's actual effects. Both council members came up with their own scenarios and examples to show how much a taxpayer would have to pay under the estate tax. Both Wilson and Kane accused each other of distorting the facts and misunderstanding the complicated tax.

In another vote, the council cleared up ambiguous language in the voter-backed initiative to call a statehood constitutional convention. The measure, as amended, would allow elected and appointed city government officials to run for slots as convention delegates. Also, the council wiped out language that may have required a second vote on the initiative.