The board of governors of the British Broadcasting Corp. today canceled a documentary on Northern Ireland, scheduled to be aired next week, after the government asked for its withdrawal on grounds that it was "against the national interest."

The government-appointed board overrode approval of the program by the BBC management, saying it would be "unwise" for it to be "transmitted in its present form." The program, entitled "At the Edge of the Union," includes an interview with a man it says is believed to be chief of staff of the outlawed Irish Republican Army.

The board called for "further discussions" with the government, and Home Secretary Leon Brittan said he would be happy to meet on "the issue of terrorism and the way it is handled on television." Brittan has acknowledged that he has not seen the program, but was relying on "press reports" of its contents.

Both the government's public request and the board's acquiescence were unprecedented in the history of the corporation. Although state-owned, the BBC has prided itself on independence and has a reputation for objectivity. The government's power to stop a BBC broadcast has never been used.

Today's decision provoked an immediate outcry by opposition politicians as well as outside commentators, and expressions of shock from BBC staff members. They charged political interference and censorship, and journalists at the corporation met to consider union action.

Asked tonight if the government had influenced the board's decision, Chairman Stuart Young said, "Categorically no." The program "is not going to be transmitted," Young said in a televised BBC interview, "because the climate is not right . . . and that is vital, and that's what the decision was all about."

The incident marks the first government-media controversy here since Prime Minister Margaret Thatcher two weeks ago, in the wake of the TWA hijacking, called for voluntary media cooperation in limiting coverage of terrorist actions. She said the media encouraged terrorism by publicizing it.

In a previously scheduled live television interview tonight, Thatcher drew a direct parallel between those comments and the Northern Ireland documentary. "I do not believe that any great organization like the BBC should do anything which might be construed as furthering the objectives of the terrorists and I feel extremely strongly about it."

Recounting numerous IRA attacks, Thatcher acknowledged she had not seen the program, but said, "Anything which is shown which seems to help terrorists seems to me to be totally and utterly wrong."

"We don't censor," Thatcher said. "We never do. We request." But she said she was "very pleased" with the board's response to the government's request, "And I believe that most people will applaud it."

Critics of both the government and the board insisted today, however, that the canceled program was a questionable example of what Thatcher called "terrorist publicity."

Intending to highlight the seemingly irreconcilable differences in the British-ruled province, it features interviews with principals on the two sides of the controversy. One is a hard-line Loyalist, or Protestant supporter of British rule in the troubled province.

The other is Martin McGuiness, allegedly chief of staff of the IRA, the illegal armed wing of the Roman Catholic opposition, and an elected member of the province's assembly.