An independent inquiry has been launched into the death of Mikaeel Kular, the three-year-old boy battered to death by his mother, after it emerged he had been in and out of foster care.

Fife council confirmed it had ordered a significant case review after Mikaeel's mother, Rosdeep Adekoya, admitted on Friday to killing him at their Edinburgh flat in January after becoming enraged when he fell sick, and then covering up his death.

The 34-year-old had originally been charged with murder but pleaded guilty at the high court in Edinburgh to reduced charges of culpable homicide and attempting to defeat the ends of justice by covering up Mikaeel's death, seven months after sparking one of the largest missing person searches in Scotland by falsely claiming he had wandered off from home.

Mikaeel's body was found four days after he died, wrapped in camouflage material and folded into a strapped-up suitcase. The suitcase, disguised by branches, had been left in woods behind a bungalow in Kirkcaldy, Fife, belonging to Adekoya's parents and sister.

With Adekoya now facing a lengthy prison sentence, serious questions emerged about Scotland's social work system after it was revealed that Mikaeel and his twin sister, now four, were taken into foster care in Fife several times because of their mother's neglect, emotional ill-health and erratic lifestyle.

Adekoya, who was brought up in Kirkcaldy and had been living there and in Edinburgh, had alarmed her parents by leaving her five children without proper supervision or dumping them on other family members while she went drinking in Edinburgh.

Mikaeel Kular, whose body was found four days after he died in woods behind a bungalow belonging to Adekoya's parents and sister. Photograph: Police Scotland/PA

She persuaded Fife social workers to allow her full custody of the twins and in August 2013 she moved back to Edinburgh with her estranged husband Omotoso Adekoya, father of her oldest children, aged nine, seven and six.

In December 2013, social services stopped monitoring the family. The court heard that Mikaeel, whose father was one of his mother's childhood friends, was seen to be a "healthy, happy little boy".

Fife council confirmed on Friday that its social workers would be interviewed by the independent inquiry, expected to be chaired by a senior expert from another local authority.

The review, due to report by December, will include police, the NHS, courts and child protection officers in Fife and Edinburgh and include evidence uncovered by the police investigation into Mikaeel's death.

Annette Bruton, chief executive of the Care Inspectorate, Scotland's social work regulator, said she expected the investigation to be "comprehensive, thorough and robust‚" and to establish whether Mikaeel's death could have been prevented.

Hinting that the history of Fife and Edinburgh's collaboration on the Adekoya family case was of particular importance, Bruton said: "There are lessons to be learned, they must be directed at preventing future tragedy. We will be monitoring carefully any recommendations from the serious case review to ensure they are implemented."

The high court heard that Adekoya, a self-employed beautician, had repeatedly assaulted Mikaeel because he had been sick after a trip to a Nando's restaurant.

Advocate depute Alex Prentice, prosecuting, told the court that Mikaeel had died from abdominal trauma after suffering more than 40 injuries, inflicted by being smacked and punched, hit with other blunt instruments and struck against hard objects at home.

He died from severe internal injuries two days after his mother had violently assaulted him after he was sick a third time on Sunday 12 January; she dragged him to the bathroom and inflicted the fatal blows as he lay over the bath.

Prentice said Adekoya beat Mikaeel heavily on his back as he lay over the edge of the bath. "It's likely that the internal damage was inflicted during this last beating," the prosecutor explained.

The boy's condition worsened over the next few days, and he was kept off nursery. She assaulted him again on Monday after he was again sick, and the child became listless. She failed to call for medical help or take him to the doctor, because his body was so heavily bruised.

On Tuesday, after becoming quiet and giving a "limited response‚" to his mother, Mikaeel died. Adekoya found his body on his bedroom floor after waking her children up on Wednesday morning. His injuries included including trauma to the brain, haemorrhage to his spinal cord and injuries on his arms, back, chin and cheek.

"He would have been in significant pain but was put to bed," Prentice told thejudge, Lord Glennie. "The pain would have increased significantly while Mikaeel became dangerously ill and finally dying as a result of the injuries inflicted upon him by the accused. It was during that night that he died."

It emerged that Adekoya, a single parent with four other children from two separate partners, had suffered long-standing mental health problems including depression, stress and anxiety before she lost control that weekend. Her father died in front of her when she was 16, the court heard.

She had made repeated internet searches for questions such as "I find it hard to love my son", "love all of my children except one"‚ "why am I so aggressive with my son".

Prentice said: "The Crown accepts that the accused had no intention to kill Mikaeel and that the assault perpetrated upon him, although severe, fell short of the wicked recklessness required for murder."

On Wednesday morning, after taking Mikaeel's twin sister to nursery she then drove to Fife with his body in the boot of her black Vauxhall car, before hiding it behind her sister's home. At 7.15am on Thursday Adekoya reported Mikaeel missing to police.

Police officers who arrived at the family's flat found her "very upset and distressed". She claimed Mikaeel had got up during the night, got himself dressed, wearing pyjamas and winter hat and gloves, and climbed on a chair to open the front door before letting himself out.

Police Scotland launched a missing persons appeal, which led to one of the largest and most heavily publicised public searches Edinburgh has seen.

With churches opening their doors to feed and shelter volunteers, the search was given greater urgency by the cold January weather. The police were fearful that Mikaeel could be suffering from exposure with night-time temperatures close to zero.

Scores of officers using dogs, aided by specialist search teams including the coastguard and mountain rescue teams, and hundreds of local residents scoured properties, streets, woods and the nearby shoreline.

The high court heard that inconsistencies in Adekoya's story became clearer on Friday. The police suspected her account. She broke down during a police interview and told officers: "It was an accident and I panicked. I am going to go to the jail." Mikaeel's body was recovered shortly before midnight that night.

Adekoya is due to be sentenced on 25 August.