Three funerals had to be held for a baby after police failed to return all of her body parts, it has emerged.

Leah Aldridge was killed by her father in 2002. But her family were unable to properly lay her to rest after police repeatedly failed to return her body parts.

The family’s MP, Chris Green, asked the prime minister to launch a public inquiry, saying the family had no confidence in Greater Manchester police after some of Leah’s remains were found for the second time.

Speaking at prime minister’s questions, Green, who represents Bolton West, said: “[Leah’s family] have no confidence in Greater Manchester police or the police and crime commissioner, the mayor of Greater Manchester [Andy Burnham], that they now have finally allowed the family to lay their daughter, Leah, to rest.”

Leah, from Atherton near Manchester, died aged five weeks. The baby, who had a cold and was not sleeping, was shaken to death by her father, Andrew Ashurst.

She died in hospital on Christmas Day in 2002. Ashurst was jailed for three years for manslaughter in 2004.

A postmortem found that she had been violently shaken, causing a catastrophic brain haemorrhage. After the coroner and Greatest Manchester police finished their investigation, the child’s body was returned to the family for a funeral.

But last year they were shocked to be told the police had not returned all of Leah’s body parts.

On Wednesday, Green told of their devastation at having to hold a third ceremony for their daughter. “Only a few weeks ago, yet more body parts were discovered by the police and the family had to go through the ordeal of a third funeral,” he told parliament.

There were gasps in the house as details of the case emerged and many MPs were seen shaking their heads. Theresa May described it as an “absolutely terrible case” and expressed her sympathies to Leah’s family for their “prolonged trauma”.

She said: I’m sure he will have felt from the reaction from members across the house, as he set out the details, that we all want to express our deepest sympathies for what is a prolonged trauma they have had to endure as a result of the way this has been handled.”

She told the House of Commons that the deputy mayor of Greater Manchester had contacted the Human Tissue Authority about the case. She added that Home Office officials would meet Greater Manchester police and the National Police Chiefs Council.

A spokesman for the mayor’s office said it was a “tragic and deeply distressing matter”. He said the mayor was contacted about the case in August, had discussed it with the deputy mayor and the chief constable and had written to Leah’s family to offer his full support.

“This is being treated with the upmost seriousness and the mayor and deputy mayor’s firm focus continues to be supporting the family until they get the answers they need,” he said.

Det Ch Supt Mary Doyle of Greater Manchester police explained that parts of Leah’s body were kept as a sample alongside a further 180 samples for “investigative reasons”.

In September 2016, the force visited dozens of families. “Each family was told about the sample held that was taken from their loved one, and how they were taken for investigative reasons,” Doyle said. “They have been given a range of options for sensitive disposal of the samples, all of which GMP will pay for.

“This is a deeply sensitive and private matter for the families affected, and the decision to contact them was not taken lightly. In fact, it was a decision we agonised over with a number of independent advisory groups, partner agencies and other professionals.

“We will, of course, cooperate with any inquiry, as we believe it is important the process is as open and transparent as possible.”