Sir Cyril Smith was a sex abuser of boys in the late 1960s, police say.
The Crown Prosecution Service also said he should have been charged with the crimes more than 40 years ago.
Greater Manchester Police (GMP) said the boys "were victims of physical and sexual abuse" by the late Rochdale MP.
Despite not being charged, after inquiries in 1970 and the 1990s, the CPS said procedural changes meant a prosecution would have been pursued today.
In a statement, Sir Cyril's family said they were "deeply saddened and concerned" by the allegations "made so long after Sir Cyril's death and at a time when he is no longer able to defend himself".
'No prospect of conviction'
Evidence now made public indicates that a file compiled by Lancashire Constabulary in 1970 contained allegations made by eight men that they had been subjected to indecent assaults by Sir Cyril when they were teenagers.
It was handed to the first Director of Public Prosecutions (DPP) Norman Skelhorn, and contained statements that were very similar in nature from the eight alleged victims, the CPS confirmed.
However, the only documentation still remaining is a one page letter Mr Skelhorn wrote to the Chief Constable of Lancashire on 19 March 1970 about Sir Cyril, who died in September 2010.
In it, he stated: "I do not consider that if proceedings for indecent assault were to be taken against Smith, there would be a reasonable prospect of conviction."
Nazir Afzal, chief prosecutor for the CPS in the North West, has now accepted that this "way of thinking bears little resemblance to how such cases are assessed today".
"The decision made by the CPS in 1970 would not be made today," he admitted.
The Lancashire Police investigation centred on offences committed between 1961 and 1965 when the boys were either living at Cambridge House Children's Home or were "dependent on Cyril Smith for either employment, financial support or some sort of guardianship", said Mr Afzal.
He confirmed that when the CPS carried out a review of the case in 1998, it was decided no proceedings would be brought against the MP, because he had been told in 1970 that he would not be charged, a decision that could only be reversed if new evidence was unearthed.
The original decision not to proceed was down to the fact there was no independent corroboration of the alleged victims' evidence, the CPS said.
"[But] victims of historical sexual abuse are entitled to justice, and prosecutions that would not have been attempted in the past are now brought successfully," the CPS said.
GMP has worked extensively with the Lancashire force since new allegations against Sir Cyril emerged last month, and has confirmed it has taken "overall command" of the investigation.
Assistant Chief Constable Steve Heywood said: "We are now in a position to say that on three separate occasions, files were passed to first the DPP and then the CPS containing details of abuse committed by Smith, but on each occasion no prosecution was pursued.
"We believe that if the same evidence was presented to the CPS today there would have been a very realistic prospect that Smith would have been charged with a number of indecent assaults, and that the case would have been brought to trial."
Blue Plaque removed
He added: "Smith cannot be charged or convicted posthumously. From the overwhelming evidence we have, it is right and proper we should publicly recognise that young boys were sexually and physically abused, and we will offer them as much support as they need should they wish to speak to us."
Lancashire Councillor Alan Neal, who revealed in October that he was physically abused as a boy, by the MP, said: "This is good news for all of those boys who have suffered for so long over the years."
Investigations were stepped up two weeks ago when current Rochdale MP Simon Danczuk (Labour) made a parliamentary statement, calling for a new police inquiry.
Rochdale Council has removed a blue plaque to Sir Cyril from the town hall as a "neutral act to prevent vandalism".
ACC Heywood also said the force will investigate "any evidence that anyone was complicit in the abuse that is still alive today."
Sir Cyril's family said: "The allegations are not new and were investigated by Lancashire Police, Greater Manchester Police and the DPP.
"We cannot comment on why the DPP took the decision not to bring charges at the time or on subsequent occasions.
"We have no wish to be involved with any further trial by media, but we will fully co-operate with any further investigation conducted by the police and/or the CPS."