Steel, who was leader of the Liberal Party and Liberal Democrats from 1976 to 1988, failed to pass on allegations against prominent colleague Cyril Smith because it was “past history”. He later recommended Smith for a knighthood.
He told the Independent Inquiry into Child Sexual Abuse (IICSA) that, because allegations against Smith had arisen before he joined the party, he saw “no reason, or no locus to go back to [it]”.
The inquiry, which published its report on Tuesday, added: “This failure to recognise the risks was an abdication of responsibility, and the fact the offences were non-recent was irrelevant.”
On Tuesday the inquiry accused the political establishment having turned “a blind eye” to allegations in Westminster.
It said high-profile politicians were protected from police action as party whips sought to avoid “gossip and scandal” that would damage the parties.
Smith was accused of a series of abuses at the Cambridge House hostel, Rochdale, in 1969.
In a statement this afternoon, Steel, who was first elected as an MP in 1965, was critical of how the IICSA conducted its investigation.
“Contrary to some reports, at no point did Cyril Smith admit to me the truth of the allegations,” he said.
“Knowing all I know now, I condemn Cyril Smith’s actions towards children.
“Children deserve protection from predators, especially those in authority. Dealing with such cases is the IICSA’s legitimate role. I believe in the highest standards of human rights, particularly for young and vulnerable people.”
He added: “I regret the time spent on pursuing Leon Brittan, Lord Bramall and others, who it is clear had done no wrong. Not having secured a parliamentary scalp, I fear that I have been made a proxy for Cyril Smith.”
But Richard Scorer, a specialist abuse lawyer, who represented eight of Smith’s victims, said: “Steel’s total inaction after being told by Smith himself that he had molested young boys is unforgivable, most of all for those victims whose abuse he could have stopped.
“To suggest Steel is a scapegoat, as some have done, is grasping at straws – a pathetic attempt to excuse a man who admitted he knowingly turned a blind eye to Smith’s crimes. He is not being blamed for them but for his own failure to stop Smith when he had the chance.”
Welcoming the news of the resignation, Scorer added: “What my clients would really like to hear is an honest and sincere apology that, as vulnerable youngsters, he let them down, and a promise from those in power that lessons will be learned from this and the mistakes of the past will not be repeated.”
The Liberal Democrats said they were “constantly” working to improve party complaints procedures.
A spokesman for the party said: “Cyril Smith’s acts were vile and repugnant.
“We have nothing but sympathy for those whose lives he ruined.”
In its report today, the IICSA found no evidence of an organised paedophile ring, or that party whips had deliberately suppressed information about child sex abuse.
Inquiry chair Professor Alexis Jay said: “It is clear to see that Westminster institutions have repeatedly failed to deal with allegations of child sexual abuse, from turning a blind eye to actively shielding abusers.
“A consistent pattern emerged of failures to put the welfare of children above political status, although we found no evidence of an organised network of paedophiles within government.”