Up to 57 families were not given the ashes of babies who were cremated, an investigation has found.
A report into Hull City Council's handling of infant cremations said families had been given "incorrect or incomplete information" by its staff.
Tina and Mike Trowhill, whose son's ashes were scattered without their knowledge, said they were disappointed and called for an independent inquiry.
The council apologised and admitted "inconsistencies" in its records.
Hull City Council started the internal investigation after a campaign by the Trowhills and complaints from bereaved families.
In its report, the council said its bereavement services had received requests from 57 parents asking for "information relating to their babies' cremations" between November 2014 and January 2017.
The authority said: "These historic cases relate specifically to instances whereby parents were told that a baby cremation could be arranged through the Children's Hospital but there would be no ashes as a result of the cremation.
"In almost all of these cases a record has now been obtained and it has been established that, unlike in other investigations nationally, ashes were always produced."
There was "a number of historical inconsistencies regarding the checking of instructions and record keeping, in the past", the report said.
It also highlighted "a lack of clarity of appropriate consent for the cremation to take place" during the "cremation application process".
In a statement, the council said it had "put a number of measures in place" to prevent further cases including a training programme for staff, clear forms and instructions.
It also said "a bereavement midwife" had been appointed at the Women and Children's Hospital.
Mrs Trowhill welcomed the changes but said: "It's striking there are still no answers in there.
"Parents are still not being told [what happened and] where the ashes were and where they've been scattered.
"I'm still not happy. There needs to be an independent inquiry."
Trish Dalby, deputy chief executive of the council, said: "Our priority is to ensure that families do not have to go through similar experiences in the future following the death of a baby, and we will continue to work with all parties to ensure the necessary changes are comprehensively implemented."