The Museum of London is considering reburying its collection of 17,000 skeletons on ethical grounds.
Skeletons are an important source for research
The bones, unearthed in London over the last 30 years, are currently stacked from floor to ceiling in the storerooms.
In an interview in The Times newspaper, museum director Jack Lohman said it was "an ethical issue" and that the skeletons deserved a final burial.
But some academics are opposed to the idea, claiming they are an invaluable resource for historical, sociological and medical researchers.
Hedley Swain, head of early London history and collections, said: "The people making decisions should ask themselves whether they would feel comfortable about their bodies being dug up one day and stuck in a cardboard box."
But James Steele, chairman of the British Association for Biological Anthropology and Osteoarchaeology, said: "Reburial may mean the loss of any future potential to analyse the material."
The museum wants the bones to be given a Christian burial - perhaps in the crypt of a disused church or consecrated ground - after they have been properly studied and documented.
Many had Christian burials, judging from the artefacts found beside them or because they were dug up at monastery sites.
The fate of the non-Christian skeletons will also have to be considered.
The museum, which attracted 363,000 visitors last year, houses one of the world's most important collections of Roman, medieval and post-medieval skeletons.