It follows a meeting on Monday with Bradley with survivors who told them that it could take up to two years for compensation payments to be made.
Victims have accused Bradley of “emotional blackmail” after they said she told them that while it was impossible to fast-track legislation through Parliament, a redress scheme could be running within six weeks if power-sharing was restored.
The North of Ireland’s six main party leaders answered four questions posed by her about the scheme, only for a further 11 to then be asked of them.
The parties united last night in rounding on the Secretary of State over the additional questions and accused her of employing delaying tactics.
They had earlier agreed to increasing the minimum payout to those abused from £7,500 to £10,000.
Bradley held the series of meetings with victims to explain her position.
She told them there could be a lengthy legislative process at Westminster due to the suspension of power-sharing.
Jon McCourt, who was abused at St Joseph’s Children’s Home in Derry, expressed his fury at Mrs Bradley’s stance.
“It is a form of emotional blackmail. And it doesn’t just hurt those of us who were present at the meeting but others, who are more vulnerable, whom we have to deliver this message to,” he said.
“I am not saying there is no hope but there is no hope right now and there is no hope in three months, and there is a possibility there may not be hope of seeing this resolved for a further 12 months.”Mr McCourt, who leads the Survivors North West group, said the request for an interim payment for victims who were elderly or terminally ill “who would not make it for another 12 months” had been refused.
“All we can tell them is we’re fighting the best we can. We’ll take it to the end but we’ve no idea when that end will be. By the time we get there, we won’t have as many people as we have today.”
Mr McCourt added: “We are being used as a political pawn in a game to force a coalition of the unwilling around a table.”
In January 2017 compensation payments for victims, a public apology, a memorial at Stormont and care packages were among the recommendations made by retired judge Sir Anthony Hart in his public inquiry into institutional child abuse.