A second police force should take over the investigation into the death of toddler Poppi Worthington in an attempt to " salvage some prospect of justice", ministers have been told.
Former shadow home secretary Yvette Cooper also insisted there is no need to wait for the outcome of the second inquest into her death.
She joined Labour MP John Woodcock ( Barrow and Furness) in calling for the police investigation to continue under the lead of an outside force.
Mr Woodcock urged ministers to order a thorough independent investigation similar to those conducted into the deaths of Peter Connelly, known as Baby P, and Victoria Climbie.
He said such a move would show the Government "values Poppi's life as greatly".
Paul Worthington was found to have sexually assaulted his 13-month-old daughter.
High Court family judge Mr Justice Peter Jackson ruled that the 48-year-old - on the balance of probabilities - "perpetrated a penetrative ... assault" on Poppi.
But he will not face criminal action unless new evidence comes to light.
Poppi collapsed with serious injuries at her home in Barrow-in-Furness, Cumbria, in December 2012 and was rushed to hospital, where she was pronounced dead.
Cumbria Police have been criticised for their handling of the case.
Speaking in the Commons, Mr Woodcock told Home Office minister Karen Bradley: "The combined failure of several agencies is every bit as serious as those which contributed to the deaths of Victoria Climbie and of Baby Peter in Haringey.
"Will the Government make clear that it values Poppi's life as greatly by ordering now a similarly thorough independent investigation into how the failings happened?
"Will they, as the second inquest is continuing, order a separate force to come in and take over the investigation into Poppi Worthington's death to try to salvage some prospect of justice for her life?"
Labour's Ms Cooper added to Ms Bradley: "Can I urge you to keep pursuing this case yourself and not to be deterred by the process that is taking place, and also particularly to clarify what is the situation about the police investigation now because surely we don't need to wait for the inquest for police investigation to be continuing?
"The (Independent Police Complaints Commission) is, I understand it, just verifying whether the police previously did the right job or not.
"What we need is a police investigation now into this individual case and could that be done by an alternative police force?"
Opening her reply to an urgent question on the case, Ms Bradley said the IPCC has investigated Cumbria Police's handling of the original investigation.
She said: "The IPCC report is completed but cannot be released yet so as not to prejudice the second inquest."
Ms Bradley added: "This Government is committed to tackling child sexual abuse but I know that's of little consolation to the family of Poppi Worthington."
Mr Woodcock outlined his questions for an inquiry and the continuation of the police investigation involving a new force.
He added: "And what will the Government do to ensure the safety of the Worthington children and all of the children in the community in Barrow, given that Paul Worthington is still walking free?"
Ms Bradley said there was an investigation by Ofsted in 2015 into Cumbria social services, which found it was "inadequate".
She added: "The Department for Education is currently in the process of intervention into Cumbrian social services to ensure that child social services are properly working in Cumbria and that all children in Cumbria have the support and the protection that they so rightly need.
"We do need to learn lessons from this case but we need to wait for that second inquest.
"The Attorney General has granted that second inquest and until that inquest is completed we will not have the full facts.
"You will also know that, in order for the case to be reopened, new evidence will need to come to light, which may or may not be the case depending on the IPCC inquiry and also the second inquest.
"But this is an operational matter which I as the minister will not be able to intervene on."
In response to Ms Cooper's questions, Ms Bradley insisted she will "get to the bottom" of Poppi's death and learn all lessons.
She said: "We owe it to Poppi Worthington; we owe it to all other children in that situation."
Ms Bradley reiterated that there would need to be fresh evidence for a new police investigation but offered to write to Ms Cooper to provide more information when she receives it.
Labour called for the IPCC's draft report to be released although M Ps later heard it appears to have been leaked to the media.
Labour MP Sue Hayman (Workington) told Ms Bradley: "One thing that concerns me about the IPCC report is that it appears to have been leaked to the press, which is of a great concern."
Mr Woodcock could be heard saying: "The BBC have it."
In reply, Ms Bradley said: "I'm not aware that it's been leaked but I will look into that matter and that maybe when I meet (Mr Woodcock) we could have a discussion then when we've got more information about what has happened.
"But I agree, if that report has been leaked that is absolutely shocking. That should not have happened."
Shadow attorney general Karl Turner also supported calls for a "separate police investigation" by a new force.
Conservative former children's minister Tim Loughton said of Poppi's case: " This sounds like a depressingly familiar catalogue of failure and cover-up."
Stewart Jackson, Tory MP for Peterborough, asked Ms Bradley: "Isn't it troubling though, and don't we need a review into the interface between the family courts and public agencies, that the latter used public money in order to try and stifle debate and hide transparency and openness in respect of this using the family courts?
"Isn't it time we reviewed that because openness and transparency is the best disinfectant to solve these sorts of issues in the future, to make sure something as terrible and awful as this never happens again?"
Ms Bradley said she would discuss the issue with Lord Chancellor and Justice Secretary Michael Gove as it was a matter for his department.
Keith Vaz, Labour chairman of the Home Affairs Select Committee, said: "The crucial relationship is between the police and social services and the crucial process is that information should be passed on immediately.
"If that is done then these terrible acts can be discovered even more efficiently."
Ms Bradley said Mr Vaz had made an "incredibly important point", noting that work is ongoing to improve this in order to protect children.