Negotiations have begun breaking down on cases pending at a key Federal Trade Commissiion office as a result of an administration proposal to phase out all 10 FTC regional offices, a top FTC official says.

In addition, the directors of these regional offices say that ongoing investigations involving industries as wide-ranging as the food and computer industries would be jeapordized by the proposed budget cuts.

The disclosures are contained in a series of letters submitted to Rep. Benjamin Rosenthal (D-N.Y.), whose consumer subcommittee is investigating the Reagan administration budget cut proposals for the FTC and the Consumer Product Safety Commission. Although the administration has backed off on its efforts to cut back the commission by phasing out its antitrust authority, FTC officials say the closing of the regional offices over three years also could have a devastating effect on ongoing cases.

Perhaps the most graphic illustration of the impact of the budget cuts on the agency is contained in a letter sent to Rosenthal by Leroy Richie, director of the FTC's New York regional office, who noted the recent collapse of settlement talks concerning antitrust and consumer protection cases handled by that branch of the agency.

"We are . . . already experiencing the breakdown of negotiations in matters where discussions are well under way and where quick settlements had been confidently expected," Richie wrote in a March 10 letter.

"I expect that this trend will continue. Although the agency and this office have in the past experienced dilatory tactics, never before have prospective respondents been presented with such a compelling motive for delay," he wrote.

Richie also warned that unless FTC investigations handled at the regional level are completed before the offices are closed -- as soon as the end of fiscal 1983 under the proposal by the Office of Management and Budget -- those cases will have to be ended.

Further, the FTC official also warned that if Congress adopts the FTC proposal and agrees to phase out the regional operations it is unlikely that "significant investigative efforts or any litigation could long continue after the announcement."

Richie's warnings are just one glimpse of the impact the budget cuts are likely to have on a series of major cases now being handled by those offices. Among the other matters the cuts would jeopardize are:

A major investigation by the San Francisco office of "rampant" unfair and "abusive practices" by the computer industry and in particular two major California firms. The director of that office said that case would be jeopardized if the expertise in her office is not retained.

Eighteen antitrust investigations from the Los Angeles office also would be jeopardized, includiang a probe of the motion picture industry, which is focusing on the difficulties independent film producers face in selling their films abroad. Also in question under the budget plan would be the office's nationwide investigation of the real estate brokerage industry. b

Antitrust investigations of two major tire companies -- one domestic and the other foreign -- and other probe of the payment practices of large retail companies, both run out of the Cleveland regional office, also would be affected.

A nonpublic investigation of the Water Pik Division of Teledyne Industries, which involves allegations that the company "granted preferential prices to its largest customers," would be subject to curtailment, the director of the Denver office warned.

The regional officials, while predictably critical of efforts to shut down the operations they manage and presumably unhappy about the prospect of losing their jobs, argue that the expertise about local industry and consumer problems in the regions cannot be transfered to Washington.

Further, it will be very difficult, they say in the letters, for the Washington FTC staff to become immersed quickly in the complex ongoing probes and court cases. In addition, work on those cases from FTC headquarters will be costly as a result of travel and document shipping costs, the officials say.

The budget, the OMB ordered the FTC to submit, calls for the commission's fiscal 1982 budget to be cut from an earlier recommendation of $77 million to $69.4 million. Over the next four years, the budget would be cut to 60.4 million. The commission now has 1,771 staff members, and that figure under the plan would be cut to 1,675 this year.