Planning Research Corp., the large Washington-based consulting and computer services firm, yesterday announced a dramatic cutback in its British operations that could wipe out the company's entire second-quarter profit.

The company, which already is in the midst of a major restructuring program, blamed the cutback on the British recession. A company spokesman, Marvin Katz, said PRC had terminated about 75 members of its British staff of 110 people.

Although the precise impact of the cuts was not known, company officials said the British action would probably offset profits from the rest of PRC's worldwide operations for the fiscal second quarter which ends Dec. 31.

The company reported profits of $1.46 million or 22 cents a share for the first fiscal quarter and profits of $1.29 million, equivalent to 19 cents a share, for the second quarter last year. The company has not made a public projection on its second quarter results, although it is likely PRC would have reported profits of at least $1 million.

Katz said he could not estimate precisely what the loss would be as a result of the British cutbacks, since PRC officials were still working out the tax and corporate balance sheet consequences of the sharp scaling back of its European activities.

"The market for our U.K. computer business has not developed as we expected," said John M. Toups, PRC's president and chief executive officer. "With the depressed economic conditions there showing no signs of improvement, we decided to reduce our operations rather than wait an unknown period for the business to improve."

Toups said the company's strategic planning process, which he and PRC Chairman Robert Sarnoff have developed as a means to refocus the company's diverse operations, has indicated that the PRC computer systems do not have the potential of other company commercial software projects.

PRC has more than 250 offices in 40 countries and employes about 6,800 people. For the 1979 fiscal year the company reported profits of $5.5 million on revenues of just over $280 million.

When PRC announced an 11.6 percent drop in 1980 first quarter profits compared to 1979 profits for the same time period, the company also noted that revenues had jumped by 17.5 percent compared to 1979 quarter. In that announcement last month, the company said that expansion costs for PRC's Western Europe computer operations had been higher than anticipated, cutting into quarterly revenues.