It was the last of a long series of television interviews that Prime Minister James Callaghan had to endure during the month-long election campaign. Before the campaign, he had not even held press conferences very often during his three years as prime minister.

Callaghan had undoubtedly heard disappointing news about his party's ebbing strength in the last pre-election opinion polls before he went to the studios of Britain's commercial Independent Television News (ITN) yesterday to tape the interview with political reporter Peter Rose.

He became irritated when Rose persisted in questioning him aggressively about labor union conflict in Britain, an issue that has hurt Callaghan's Labor Party during the campaign.

"What if the unions can't control their own militants?" Rose persisted. "So there are no-circumstances in which you would legislate?"

"I didn't say anything of the sort at all," Callaghan answered angrily. "I'm not going to take the interview any further. Look here, we're been using five minutes on industrial relations. You've had five questions on industrial relations. You said you would do prices.

"I'm just not going to do this . . . That program is not to go . . . This interview with you is only doing industrial relations. I'm not doing the interview on that basis. I'm not going to do it."

"Don't argue with me," Callaghan shouted as he left his chair and stalked out of the studio. "I'm not going to do it."

Callaghan calmed down only when network officials said they would start the interview over, Rose would not push him on industrial relations, and Callaghan's blowup would never be shown. The prime minister agreed and viewers here saw a subdued, bland final campaign interview last night, highlighted only by Callaghan's statesmanlike promise to try again for a political settlement of the sectarian conflict in Northern Ireland if he remained in office.

But, unknown to Callaghan, NBC Television taped the aborted interview. Its bureau here monitors and tapes all ITN news show and uses selected excerpts on its new programs in the United States. NBC used 15 seconds of the tape showing Callaghan storming out of the aborted interview as part of long segment on the British election campaign on its network news show last night.

When British correspondents in the United States saw it and called London, the news media here and British public found out about the incident. Labor Party headquarters "protested strongly" today to ITN, which issued a public apology and said it never expected NBC to show the scene in the United States.

"ITN has expressed its regret to the prime minister," a spokesman said today. "The prime minister had objected to an interview because he felt it was not sufficiently wide-ranging. The interview was done again. This is part of the give-and-take that happens from time to time in interviews."

It also happens that there is a long-standing agreement between both British television networks-noncommercial BBC and commercial ITV which ITN is a part-that the prime minister and other senior politicians can stop the showing of any interview they do not like. Former prime minister Harold Wilson did it some years ago.

Leading politicians also can veto the use of interviewers they do not like, as Conservative Party leader Margaret Thatcher did earlier in this campaign. CAPTION: Picture, Pensioners from the Chelsea Royal Hospital outside London-wearing red uniforms and pillbox hats-arrive by bus to cast their votes in the general election. AP