Coroners Act 2006, s 42
The coroner has to release the body as soon as they’re satisfied there’s no reason to withhold it from the family. They’ll usually authorise its release (by signing an Order for Disposal of Body) within 24 hours after any post-mortem. The body can then be released to the family to be buried or cremated.
If the coroner has decided a post-mortem isn’t needed, the coroner has to wait for 24 hours after notifying the police of this decision before releasing the body, although the police can allow the coroner to release it before this. There could also be delays if specialists (other than the pathologist) need to be called in. However, usually the body should be released with no more delay than would normally occur if a doctor signed a Medical Certificate of Cause of Death.