MPs have backed a proposed law which would deny killers parole if they refuse to reveal the location of their victims' bodies.
It follows the campaign to change the law, which reached more than 343,000 signatures.
The law is named after 22-year-old murder victim Helen McCourt, whose body has never been found after she was abducted and killed by Ian Simms 28 years ago.
"One is bound to ask in what sense a murderer, who is content to torment the families of their victims in such a way, could ever have earned their freedom," Mr McGinn said.
"The introduction of Helen's Law is the only chance the McCourts and families like them have of securing some peace, and the justice they deserve."
Mr McGinn said since 2007, there have been 30 murders across England and Wales where no body has been recovered.
The Unlawful Killing (Recovery of Remains) Bill was adopted by the House of Commons without opposition, and will now progress to its second reading on Friday, February 3.
However, without the support of the government, the bill is unlikely to ever become law.
Here we profile some of those whose bodies have never been found.
Helen McCourt was abducted and killed in 1988 near Billinge, just outside Wigan.
Her killer, Ian Simms, was convicted by overwhelming DNA evidence of the murder.
But the former pub landlord never admitted what he did or disclosed the whereabouts of the 22-year-old's remains.
Keith Bennett was 12 years-old when he was snatched by Ian Brady and Myra Hindley in June 1964, before being murdered along with four others and buried somewhere on Saddleworth Moor near Manchester.
Keith's mother Winnie Johnson made repeated calls for Brady to reveal the location of her son's grave but died in August 2012 without being able to fulfill her last wish of giving her son a proper burial.
Jane Harrison, from Islington in north London, was 32 when she went missing in June 1995.
Her former boyfriend, Kevin Doherty, was sentenced to 12 years in prison in 2013 after being convicted of her manslaughter.
Despite pleas from Jane's family, Doherty, now in his 60s, has never revealed where he concealed her body.
April Jones was murdered by Mark Bridger in Machynlleth, north Wales in October 2012.
Bridger, who was sentenced to life in prison, has never revealed what he did with the five-year-old's body.
During his trial, the jury was told bone fragments from a human skull were discovered in the fireplace at his home, which has since been demolished.
Paul Morson, from Merseyside, was murdered in what the Crown Prosecution Service described as a "vicious attack" in June 2011.
More than a year later, Raymond Brierly and John Burns were convicted of his murder.
It is believed Mr Morson was killed at Brierly's house in Whiston, where forensic analysis showed plastic sheeting had been nailed to the wooden beams and skirting boards, then removed, showing a disturbing level of planning.
Brierly, who claimed he had killed Mr Morson while acting in self defence, told the court his body had been dumped in the River Mersey.
Despite extensive searches, his body has never been found.
Mr Morson's family will be joining those of other victims in the House of Commons public gallery on Tuesday to hear Mr McGinn's arguments in favour of the Unlawful Killing (Recovery of Remains) Bill.