Mr Gerry Conlon says the apology issued to those wrongfully jailed for carrying out the Guildford and Woolwich bombings by the British Prime Minister Tony Blair exceeded expectation.
Emerging from the Commons after a meeting with Mr Blair, Mr Conlon and the other family members held aloft written copies of Mr Blair's apology.
Amid a huge scrum of reporters and cameramen, Mr Conlon said: "He apologised profusely and he was physically taken aback by the suffering that we have all suffered."
"Tony Blair met us privately, he spoke to every one of us, he took time, he listened to us, he exceeded our expectations in apologising, he said it was long overdue.
"I asked why we hadn't received the same treatment as John McCarthy, Terry Waite and Brian Keenan, and he said he would make sure that we got the help that we needed.
"Because ... this hasn't ended for us. But today is the start of the end. We want parity of esteem with other victims of miscarriage of justice, and we want other miscarriage of justice victims to receive a public apology the same way we have.
"If you damage people and you can repair them, it is your duty to do that. We said that to the Prime Minister, he accepted it. He went beyond our expectations."
"Everyone has been affected by this, everyone has suffered trauma from it. And the good thing is that he has acknowledged it, and he accepts that we are in pain, that we are suffering terrible, terrible nightmares and terrible post-traumatic stress disorder."
Mrs Annie Maguire spoke briefly after the meeting, saying: "We have all suffered. And this is a great day for us, for all of us." She added: "It will help our children and their children."