Salaries for white-collar workers in the private sector went up an average of 4.1 percent between March 1986 and March of this year, according to a new Labor Department study that is part of the complex process to determine the size of the next pay raise for 1 million white- collar federal workers, including nearly 300,000 here.

The study is one of two released this week by the Bureau of Labor Statistics that will be used by the secretary of labor and the directors of the Office of Management and Budget and the Office of Personnel Management to recommend a January federal pay raise.

Although the data in the two surveys are the result of months of surveying, it will have little actual bearing on the size of the next pay raise, which, mostly for budgetary reasons, is expected to be around 3 percent.

By law, the government each year is supposed to survey private sector jobs that are similar to positions in the federal service to see how much of an increase is due white- collar workers in the federal government. Although those catch-up-with-industry raises are supposed to take effect each October, presidents can -- and usually do -- delay them until the following January. The amounts they give are usually much less than data on private wage gains indicate.

Last year, for example, data developed by the government indicated that civilian federal pay on average lagged more than 20 percent behind similar jobs for the private sector. But Reagan administration officials rejected the data as being incomplete because they excluded wages of the 12 million state and local government workers, and private firms employing most of the nation's white-collar nonfederal employes. Instead, the president proposed a 3 percent pay increase that went into effect in January. Last year federal workers got no raises.

According to the Bureau of Labor Statistics report, pay for all nonfederal civilian workers surveyed went up 3.5 percent from March 1986 to March 1987. White-collar pay increases averaged 4.1 percent; blue-collar wages were up 2.3 percent, and salaries in service occupations rose 3.4 percent. The study showed that wages of state and local government employes -- who generally trail behind federal salaries -- went up 5.3 percent for white-collar workers and 4.5 percent for blue-collar employes.

The data, which will be compared to salaries paid in government, show average salaries for accountants in the private sector ranged from $19,588 for new employes to $49,291 for supervisory personnel. Pay for public accountants ranged from $21,006 for new employes to $33,989 for journeymen.

Salaries for lawyers just above the starting level were $41,370 on average, the report said, while senior lawyers averaged $63,711.

Pay for engineers in the private sector averaged $26,355 for new employes to $78,049 for top engineers. Salaries for registered nurses averaged $21,012 for new employes to $34,383 for supervisors.

Secretaries in the private sector averaged $15,285 for beginning secretaries to $29,014 for longtime secretaries. Pay for general clerks ranged from $10,338 to $19,151, while private sector averages for personnel clerks was $13,409 for new employes to $23,130 for more experienced clerks.

The data, which take in more employes in smaller firms and reflects smaller than normal annual pay increases, are expected to be used by the Reagan administration to show that previous surveys have exaggerated the pay gap between the government and private sector.