The BBC is to air the moment columnist Matthew Parris "outed" Lord Mandelson as gay for the first time since it happened more than 10 years ago.
The slip happened in 1998 during an interview for BBC Two's Newsnight.
Mr Parris told Jeremy Paxman there were "two gay members of the Cabinet at least... Chris Smith is openly gay and Peter Mandelson is certainly gay".
The recording, to be played during a Radio 4 interview with Lord Mandelson, has since been kept from the airwaves.
It includes Paxman's response: "Ah, I think we'll just move on from there, I'm not quite sure where he is on that."
Hours after the broadcast, an internal memo was issued to producers at the BBC effectively barring them from mentioning the issue.
'No political importance'
It said: "Under no circumstances whatsoever should allegations about the private life of Peter Mandelson be repeated or referred to on any broadcast."
And in his autobiography, The Third Man, Lord Mandelson says the BBC imposed a "ban" on any reference to the exchange.
But the broadcaster has now allowed it to be played during an Archive On 4 programme in which the former business secretary looks back at his career.
Lord Mandelson will say: "What upset me first of all was that they should be debating this as though it was some sort of question that hadn't been answered or that it was of some political importance.
"I had been outed by the News of the World some 10 years before in 1987 and had long since got over it and got through it.
"What I didn't accept very easily was this had suddenly become the subject of a political discussion on Newsnight, when in my view it had absolutely nothing whatsoever to do with my life as a politician or what I was doing as a minister.
"But even then I could have easily got over it I can assure you, until two hours later, after the programme had ended, there was a very aggressive knocking on the door by a journalist and when I didn't answer the door, started bawling questions through the letterbox. And I just thought, I don't need this, I don't like this, I don't approve of it and I just thought it was unacceptable journalism.
"I didn't feel any inhibition leading my life as I did. To all intents and purposes - my home, my family, my friends - there was no sort of secret, nor was there any great fuss."
A Radio 4 spokesman said Lord Mandelson had not complained about the re-use of the recording.
He said: "Meeting Myself Coming Back uses sound archive to explore important moments in a person's life and career and this was clearly a key event in Peter Mandelson's life.
"Mr Mandelson raised no objections during or after the recording of the programme."
Archive on 4: Meeting Myself Coming Back, will be broadcast on BBC Radio 4 at 2000 BST on Saturday 14 August