Co-op Funeralcare, along with MPs from the All-Party Parliamentary Group on Baby Loss, and the owners of Haltemprice Crematorium, Dignity plc, are urging Hull Council to grant the inquiry.
In July a council report admitted 57 families were not given the ashes of their babies.
Although the process produced ashes, some mothers were told by the hospital it would take care of funeral arrangements and wrongly told there would be no ashes. Others went to a funeral, but were not told about the ashes afterwards.
Campaigners feel the internal review did not go far enough and the local NHS, Co-op Funeralcare and Haltemprice Crematorium should be called to give evidence along with the council.
Managing director from Co-op Funeralcare Robert Maclachlan said: “In 2015 we committed to helping any family in Hull with questions they may have about their infant’s ashes.
“The Co-op backs Diana Johnson’s call for an independent inquiry to be established, which would further help to provide bereaved parents with closure on this issue should be fully considered.”
Tina Trowhill, whose baby’s ashes were scattered in 1994 without her knowledge, and heads Hull Action for Ashes, said the “only way” to get answers was an independent inquiry. She said: “The parents affected would have a greater level of confidence if an independent person was to look at what went so terribly wrong.”
Haltemprice crematorium, one of two sites where cremations were carried out, was owned by a different organisation before 2013, so the issues pre-date new owner Dignity.
Crematorium director Steve Gant said it was important “all families have appropriate access and knowledge of the details relating to their cases.”
However Hull Council insists a new inquiry would not provide new insights.
In a statement it said: “Firstly, we would once again like to express our deepest sympathy to all the families affected by this issue in Hull and around the country.
“Our position remains that we do not think that a local public inquiry in Hull will provide any additional information than our current investigations, or the previous inquiries in Emstrey and Shropshire, already have done.
“We have followed the recommendations made by the Ministry of Justice to publicise what we have done and their acknowledgement that we have worked extensively with the affected families and with our partners to change local processes and procedures.
“The Ministry of Justice agreed that, rather than carrying out further historic investigations, we should concentrate our resources on continuing our work and contributing to the National Working Group, which has been set up to advise the Government and other authorities on the improvement of cremation practice.”