Co-promoters Matchroom and Wasserman Boxing conceded defeat in their attempts to stage the catchweight meeting at the O2 Arena in defiance of the BBBofC declaring it was "prohibited" and "not in the interests of boxing".
The BBBofC acted after it was revealed on Wednesday that trace amounts of fertility drug clomiphene, which elevates testosterone levels in men, had shown up in a recent test by the Voluntary Anti-Doping Association (VADA).
Hearn stressed that Benn has not been suspended for the doping violation and in a statement released in conjunction with Wasserman Boxing, blamed the sport's governing body for the postponement.
"It is undeniable that the British Boxing Board of Control's decision to withdraw their sanctioning was procedurally flawed and without due process," the statement read.
"That remains a legal issue between the promoters and the Board which we intend to pursue.
"However, whilst there are legal routes to facilitate the fight taking place as planned, we do not believe that it is in the fighters' interests for those to be pursued at such a late stage, or in the wider interests of the sport.
"As promoters, we take our obligations and duties very seriously, and a full investigation will now need to take place."
Wasserman Boxing's Kalle Sauerland described the actions of the BBBofC as "totally inappropriate".
Earlier in the day, Hearn used social media to rule out appointing an overseas commission to sanction the fight but retained hope that it could still be saved.
That prospect looked over, however, when the head-to-head press conference in a Canary Wharf hotel was repeatedly delayed and Benn left the same hotel, where he had been based, with his bags packed before driving off.
The undercard fighters followed soon after, their careers put on hold through no fault of their own.
Eubank Jr took to social media to make his feelings known, tweeting: "Conor got caught using an illegal substance so the fight is off. Can't believe it.
"I really apologise to the fans and everyone that bought tickets, travelled and booked hotels, this should not of (sic) happened. He has escaped his schooling… for now."
He later added: "Just got back to my hotel room to be greeted by another random drugs test… which as always I'm happy to take. 10 years and never failed one."
Hearn refused to take questions at a press conference that was supposed to have been headlined by the fighters, instead claiming that Benn had not been treated fairly in the wake of his positive test coming to light.
"We do feel that Conor Benn hasn't been given due process, like many others in this situation before him," said Hearn, who denied reports that he had sought to challenge the BBBofC in the high court.
"We made a decision that we felt was in the best interests of the parties involved. This is a sport that is very, very dear to us. I hope you feel that the correct action has been taken."
The bout was a continuation of the Benn v Eubank feud that saw the rivals' fathers battle it out in two ferocious contests in the early 1990s.
A catchweight of 157lbs was agreed for the sons to continue the family feud into a trilogy fight, meaning Benn would have to move up two weight divisions and Eubank lose three pounds.
A new date for the fight must now be found and overseas options could be considered, with Benn, who insists he is a "clean athlete", sure to be called to a hearing at the BBBofC.
Benn said in a statement: "I am truly gutted that we are unable to make this fight happen on Saturday. And I am sorry for everyone that has been affected by the postponement.
"I am still completely shocked and surprised by this and it has been a tough couple of days. My team and I will consider the next options, including rescheduling the fight. But my immediate focus is on clearing my name because I am a clean athlete."