The British government will go ahead today with the scheduled $12.45 billion sale of its 31.5 percent interest in British Petroleum, despite entreaties from major U.S., British and other international underwriters who stand to suffer heavy losses, Chancellor Nigel Lawson announced last night in London.

But Lawson said the government was prepared to cushion the blow to underwriters by buying back shares at yesterday's market price, placing a cap on losses should the price fall further.

The underwriters, who include British firms, four major U.S. investment banking firms, three major Canadian securities dealers and Daiwa Securities of Japan, are obligated to purchase the BP shares at a price set two weeks ago, before the marketed plummeted, and could face huge losses if no other buyers emerge for the stock.

As the issue date approached, those firms mounted a major campaign to persuade the government of British Prime Minister Margaret Thatcher to postpone it. The 17 major underwriters of the issue formally requested that Lawson cancel the sale in the interests of international market stability, and, as the date approached, they intensified their efforts.

U.S. Treasury Secretary James A. Baker III and his counterpart in Canada contacted Lawson personally to express concern over what the losses could do to the still-volatile market and the solvency of the underwriters. Although Baker was said not to have asked directly for the sale to be postponed, sources said that was the clear implication of the discussion. Japanese finance officials also weighed in, according to industry sources.

According to government and industry sources in the United States President Reagan was prepared to intervene directly with Thatcher to hold back the BP share issue. Sources said, however, that Thatcher's Downing Street office indicated that she would not welcome such a call, and it was not made.

The rejection of U.S. entreaties by Thatcher, who is Washington's closest ally in Europe, was a measure of the political controversy in Britain surrounding the BP situation.

Thatcher's privatization program of selling off government-owned companies thus far has raised more than $42 billion, helping the government to cut taxes and lower its public sector borrowing requirement. Aside from the financial benefits, the program is the centerpiece of Thatcher's efforts to wean Britain away from a state-driven economy.

The opposition Labor Party, which has opposed privatization, called for cancellation of the sale and charged Lawson and Thatcher with being "driven by dogma" in their zeal to sell off government-owned companies no matter what the circumstances. In their determination "to drive through this sale," Labor spokesman John Smith said, they were placing "Conservative Party interests before the national and international interest."

Lawson, who delayed his announcement until after the close of Wall Street, told a packed Parliamentary session that the British taxpayer was "entitled to the proceeds of the issue at the offer price" of 330 pence, or about $5.68 a share, which is to be paid in three installments. In the two weeks since that price was set, the market value of BP shares has plunged, along with the rest of the international market, to close at about $4.47 yesterday.

A major reason for the government's decision was a fear that the BP price could fall even further when the market begins open trading today. There had been rumors in London that it could go as low as 35 or 40 pence, which the government feared might cause a panic.

Underwriters are obligated to purchase all unsold shares at the offer price, with a first installment of 120 pence -- about $2.06 a share -- due next Monday. Under Lawson's offer, the Bank of England would buy back these "partly-paid" shares at the market price of 70 pence, or approximately $1.20, releasing the underwriters from their commitment to pay the balance.

If all 17 major underwriters accept the offer, their loss will total about $1.7 billion. Four major U.S. financial houses who participated in the underwriting stand to lose about $100 million each, what one analyst estimated was "perhaps the largest loss on a single transaction that any has ever experienced."

The U.S. underwriters -- Goldman Sachs, Morgan Stanley, Salomon Brothers and Shearson Lehman -- had been pessimistic about the chances of persuading the Thatcher government, committed as it is to the notion of privatization, to postpone the sale and tried to put the best face on the decision.

"The transaction is moving forward. The Bank of England market support is constructive. It stabilizes the market and puts a floor under the exposure of investors and underwriters and provides some insurance as to the volatility of world markets," said a spokesman for the underwriting group.

The BP offering is expected to be the largest stock offering ever, eclipsing the sale of Conrail stock. That U.S. privatization brought in $1.65 billion. The U.S. underwriting firms have not yet put a sales price on the stock but are expected to file a registration statement today with the Securities and Exchange Commission.

Although the U.S. underwritering group could lose as much as approximately $400 million on the BP deal, tax consequences of the loss would reduce that figure to approximately $200 million, according to industry sources.

Underwriters of other British privatization stock offerings -- including Goldman Sachs, Morgan Stanley and others now facing potential losses -- have profited handsomely from those deals. If the Thatcher government had postponed the BP offering, some of the same critics who challenged the decision to go ahead would have likely faulted the opposite decision as a bailout for bankers.

Reaction by London underwriters was muted last night as they began to calculate whether they were better off taking a fixed loss with Lawson's offer -- which the Chancellor said was good for at least a month -- or holding on to BP shares in hopes that the price would go back up.

Aside from the financial losses for both individual and institutional investors and underwriters, however, the BP decision was likely to have far-reaching effects on the privatization program that is a keystone of Thatcher's government.

In an interview last night on British television, former U.S. assistant Treasury secretary Roger Altman said that U.S. investors would be highly reluctant to participate in any future British government privatization program. "If this had been a commercial transaction," Altman said, "I think the sale would have been canceled ... U.S. investors now appreciate more than they ever have that this is a different kettle of fish than a traditional commercial underwriting."