CLEVELAND (AP) _ The British Petroleum Co. PLC, expressing a lack of confidence in Standard Oil Co. management, on Thursday removed Standard Oil's chairman and president and doubled its representation on the board of directors.

But the board of directors of Standard Oil said BP has assured the Cleveland-based company that the changes are not connected ''with any suggestion of a takeover by BP of the minority shareholdings in Standard Oil.'' BP owns 55.5 percent of Standard Oil.

Robert Horton, 46, a managing director of BP and a Standard Oil board member since 1983, will succeed Chairman Alton W. Whitehouse Jr., 58, as chairman, effective April 1.

Frank Mosier, 55, the executive vice president of Standard Oil and an employee of the company since 1953, will succeed John Miller, 48, as president.

BP also increased its representation on the 14-member board of directors to six.

BP has no current intention of making an offer for Standard Oil's minority shares, the London-based company told Standard Oil.

''BP stock ownership in Standard Oil represents a very large part of BP's holdings and clearly the oil industry is entering a tough period,'' Standard Oil directors said in a statement announcing the shakeup. ''BP has indicated they felt the need at this time for a management team in which they had more confidence.''

Standard Oil's earnings plunged 79 percent in 1985 to $308 million, or $1.31 a share, from $1.49 billion, or $6.14 a share, a year earlier. The drop incurred a $771 million loss in the year's fourth quarter, reflecting the costly reorganization of a money-losing mineral business.

In addition, plummeting oil prices have put new financial pressures on oil companies.

''This is a critical time for the oil industry and especially for Standard Oil,'' Sir Peter Walters, chairman of BP, said in a statement released by Standard Oil. ''BP believes it is also an appropriate time to strengthen Standard Oil's management to cope with the difficult environment ahead.''

The move won initial cheers on Wall Street.

After the late-afternoon announcement, Standard Oil stock closed with a gain of $2.50 at $51.75 a share in composite New York Stock Exchange trading.

''It's great for the company, a real step forward for the company,'' said Suzanne Cook, an oil industry analyst at the Denver office of the securities firm First Boston Corp.

Speculation that BP planned to acquire the remaining 45 percent of Standard Oil stock grew when BP renewed a $6.5 billion line of credit last October. BP ownership of Standard Oil stock dates back to 1969 when it acquired more than a 50 percent interest in exchange for petroleum interests on Alaska's oil-rich North Slope.

Standard Oil, which has been known as Standard Oil Co. (Ohio) or Sohio, earlier this week said it was phasing out the use of the name Sohio, in favor of the name Standard Oil Co. The company is continuing to use the name Sohio to market its petroleum products in Ohio.

Horton, a mechanical engineer, joined BP in 1957. He held positions in oil supply, sales and planning and was appointed general manager of the BP Tanker Co. in 1974.

He became general manager for corporate planning of the BP Group in 1976 and was named managing director and chief executive of BP Chemical International in 1980. He was named managing director of BP in December 1983.

Whitehouse, a lawyer, had joined Standard Oil as its general counsel in 1968 and became chairman in 1978.

Miller, who has been a Standard Oil employee since 1960, has been president since 1980.

Effective April 24, E. John P. Browne, 38, will become executive vice president and chief financial officer, and J. Colin E. Webster, 49, is to be come an executive vice president.

Browne currently is group treasurer of BP and chief executive of BP Finance International. Webster is president of BP North America and a member of the board of Standard Oil. Directors also announced changes in the makeup of the board.

The six directors from outside the company will be nominated for re- election and have agreed to serve, the company said. They are: Elizabeth E. Bailey, dean of the Carnegie-Mellon University Graduate School of Industrial Administration; DeWitt W. Buchanan Jr., retired president of the Standard Oil subsidiary Old Ben Coal Co.; Douglas D. Danforth, chairman of Westinghouse Electric Corp.; William J. Delancey, retired chairman of Republic Steel Corp.; John J. Hangen, retired chairman of Appleton Papers Inc.; and Charles F. Knight, chairman of Emerson Electric Co.

The company said Richard A. Bray, an executive vice president of Standard Oil, will also be nominated for re-election to the board.

Those who will not be nominated for re-election, in addition to Whitehouse and Miller, are Dr. Glenn R. Brown, senior vice president for planning and technology at Standard Oil, and Roger Bexon, deputy chairman of BP. Both Brown and Bexon had earlier announced retirement plans.

Nominated for election to the board of directors of Standard Oil at the April 24 annual meeting are:

Browne; Basil R.R. Butler, 56, chief executive of BP Exploration; Ian G.S. Hartigan, 52, chief executive of BP Shipping; and Ken R. Keep, 57, technical director of BP Exploration.