A little-known but crucially important measure of inflationary pressures in the economy rose at the fastest rate since 1951 in the first quarter of this year, the government said yesterday.

The Labor Department reported that so-called unit labor costs - the labor cost of an average unit of production - rose at an annual rate of 18.3 percent in the January-March period.

That increase was exaggerated by some one-time-only factors - the January increases in Social Security taxes and the minimum wage, the January-February drop in production, now reversed. But analysts said that even so, the first-quarter labor costs will heighten pressure on businesses to raise prices.

William A. Cox, the Commerce Department's deputy chief economist, conceded the increase would give "some upward push" to inflation pressures. Another government economist familiar with the report called the new figures "very disturbing."

The figures came as G. William Miller, chairman of the Federal Reserve Board, confirmed to Congress yesterday that the Fed's recent steps to tighten credit and lift interest rates stemmed from its fears that inflation is speeding up and will not wind down in coming months. The theory is that higher interest rates will slow down spending and reduce demand.

At the same time, Barry Bosworth, director of the administration's Council on Wage and Price Stability warned that the inflationary spiral cannot be broken anytime soon unless big unions cut back demands for higher wages.

In remarks to reporters, Bosworth said price restraint also is important, but the major problem lies with wage demands by "the major unions." If wage settlements continue to average 30 per cent for a three-year contract, he said, "you might as well forget" about slowing prices.

Miller, in testimony before the Senate Banking Committee, suggested Congress and the administration could relieve pressure on the Fed to raise interest rates if they act themselves to slow inflation by cutting back on spending and reducing the budget deficit.

He continued to press for a delay in the president's proposed tax reductions, to next Jan. 1, from the Oct. 1 effective date Carter requested. Miller said the move would save $5 billion to $8 billion. Congress already appears to be heading in that direction.

The rise in unit labor cost stemmed from several factors, some of which economists say are temporary:

Social Security taxes rose sharply during the first three months of this year, and the minimum wage rose beginning last Jan. 1 - boosting total hourly compensation by 14 percent, the largest rise in five years.

Output levels declined 1.8 percent, largely as a result of the cold weather and the impact of the coal strike early in the year. At the same time, employers continued to expand their payrolls. The number of hours worked increased by 1.9 percent.

As a result, the productivity of American workers - that is, output per workhour, or labor's efficiency - declined at a 3.6 percent annual rate, posting its first drop since the second quarter of 1977 and the steepest plunge in four years.

When work efficiency declines, unit labor costs almost automatically speed up. The 18.3 percent annual rate posted in the first quarter was the fastest such rise since 1951. By comparison, unit labor costs rose by 6.1 percent in all of 1977.

Worker productivity has been relatively lackluster in the past several months. Outputs per workhour rose at a modest 2.3 percent annual rate in the final quarter of last year. For all of 1977, it averaged 2.6 percent.