The capstone on the largest share offering in history was put in place today when U.S. underwriters negotiated an offering price of $16.125 a share for 13.4 million shares of British Petroleum Co., Ltd., being sold here by the British government.

The $205 million raised today - after an 80 cents per share underwriting fee is deducted - together with $776 million in a separate offering of 53.4 million BP shares concluded in the United Kingdom last week, means the British government will realize close to $1 billion by reducing its stake in Britains largest industrial corporation from 68 per cent to 51 per cent.

The proceeds have been earmarked for reduction of the British government's deficit this year. The International Monetary Fund required the government to trim its external financing needs as a condition for lending Britain $3.9 billion last year to support the pound sterling.

Rather than cut further expenditures from its budget, the government elected instead to sell 66.8 million shares of BP from its holdings. These were acquired by the Bank of England in 1975 from the then-foundering Burmah Oil Co. at about one-quarter of today's offering price.

Originally, the British government had indicated that up to 25 per cent of 16.7 million of the shares it was selling would be made available as part of the oftering in the U.S. and Canadian securities markets.

But the Bank of England this morning announced that this would be reduced to 20 per cent or 13.4 million shares because of keener than expected interest shown by investors in the U.S. who were able to purchase the shares for $14.53 each.

"The decision to cut down was a political one, not motivated by investment concern," said Fred Whittemore, managing director of Morgan Stanely and Co., which was the lead manager in the underwriting group. He noted that the British government could have obtained about $1 more for each share sold through the North American syndicate.

"We could have done more than the 25 per cent even," added Whittemore. "We asked for permission, but were told we couldn't."

Besides Morgan Stanely, First Boston Corp., Goldman, Sachs and Co., Merrill Lynch, Pierce, Fenner & Smith, Inc., and Salomon Bros. served as managers for a group of more than 320 underwriters. They reached the $16.125 offering price just before the 4 p.m. close of trading on the New York Stock Exchange.

BP was the most heavily traded stock on the Big Board today, closing up 1/4 point at $16.25 after 543,200 shares changed hands.

The offering had been widely anticipated in the last few weeks, both because of its size and because of BP's investment appeal.

With sales last year of $10.6 billion, BP is the eighth largest company in the world. It has extensive petroleum interests in the North Sea and throught its ownership stake in Standard Oil of Ohio, which will exceed 50 per cent by 1978, also has one of the largest investments in Alaska's North Slope and in the Alyeska pipeline which is just now being put into operation.

Morgan Stanley's Whittemore noted that the two simultaneous, but separate, offerings in the British and U.S. securities markets represented "a historic first." And he said, "The cooperation we we got from the SEC (Securities and Exchange Commission), considering their rules, was significant."

"It's a sort of a milestone," commented another participating underwriter," not only for its size, which is very substantial, but for the technique, which is unique, and the company itself, which is 'unusual.'"