Former Association of Police and Crime Commissioners (APCC) chief executive Nazir Afzal was advised against doing so by the organisation's board.
This was because of potentially controversial policing issues that could have been raised on the show.
But Mr Afzal stepped down and appeared on the programme on 25 May.
The APCC said: "Nazir told the board that he intended to go on Question Time to discuss the recent events in Manchester.
"The board, made up of all parties, advised that it would be inappropriate for him to do so, given the number of contentious issues relating to policing which could be raised especially in discussion with politicians who were appearing and during purdah.
"He resigned from his post in order to make this appearance. We thank him for his service during his year at the APCC."
Mr Afzal joined the APCC last year.
The association said Mr Afzal signed a contract confirming that he would not do any media without the consent of the board.
This was essential because the APCC was apolitical and the role of the chief executive was politically restricted, it said.
Mr Afzal tweeted: "Given media calls I confirm that I've resigned as Chief Executive of country's police & crime commissioners. I'm not saying anything publicly."
Introduced in England and Wales in 2012, PCCs must:
Source: Association of Police and Crime Commissioners
Mr Afzal is a former Crown chief prosecutor for north-west England. It was announced he would step down in March 2015.
He led several high-profile prosecutions, including the Rochdale grooming trial.
He was awarded an OBE in 2004 for services to law and the local community,
Get news from the BBC in your inbox, each weekday morning

Media playback is not supported on this device
Paul Heatley was sent-off in the 41st minute following an off-the-ball incident with Lyndon Kane.
James McLaughlin turned the ball home from six yards midway through the second half after Sean O'Neill had parried Ruairi Harkin's initial shot.
Jordan Forsythe was dismissed for a crude two-footed challenge on Kane.
The precious point keeps Stephen Baxter's champions within four points of Premiership pacesetters Linfield.
Crusaders went into the game on the back of five straight league wins while the Bannsiders' record of just two wins in their previous 21 matches against their visitors suggested they faced an uphill task.
Rodney Brown directed a header straight at O'Neill and then Forsythe headed wide and saw a close-range effort cleared off the line by Steven Douglas.
Heatley had a low shot parried by Coleraine stopper Michael Doherty, while Jamie McGonigle raced clear and found himself one-on-one with O'Neill, who blocked the Coleraine player's shot with his legs.
Heatley was shown the red card by referee Keith Kennedy and when McLaughlin broke the deadlock, Oran Kearney's side looked to be in control.
Forsythe's 71st-minute sending-off appeared to seal the Crues' fate but O'Flynn's late intervention after a Craig McClean free-kick earned a last-gasp draw.
The head of the national body for police commissioners resigned in order to appear on the BBC's Question Time following the Manchester attack.
[NEXT_CONCEPT]
Substitute Stephen O'Flynn's final minute diving header salvaged an unlikely point for nine-man Crusaders against Coleraine at Ballycastle Road.