An investigation into Hull City Council's handling of baby cremations said 57 parents approached the authority after similar news broke elsewhere in the UK in 2014.
The council said there had been "historical inconsistencies" and a "lack of clarity of appropriate consent for the cremation to take place".
It also admitted to providing "incorrect or incomplete information" for parents when their babies died.
But it said in almost all cases a record had been found for bereaved parents who came forward and in all cremations, apart from one, ashes were produced.
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They said the historic cases related 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.
The council's deputy chief executive, Trish Dalby, said: "Bereavement is an extremely distressing time for any family to face and our thoughts are with those who have been affected by the loss of their child.
"We have endeavoured to ensure that all parents whom have come forward have been offered individual meetings, and a detailed and thorough examination of all available records, and anyone else whom has been affected by this issue should contact us so we can offer direct support and provide any detail we have on each individual loss.
"As we have done so far, we will provide any and all information that we have to the parents, irrespective of when the loss of a baby happened, and we will continue to respond to each and every inquiry.
"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."
As a result the council said measures had been put in place, including a training programme for staff and the appointment of a bereavement midwife.