Only around 40% of all deaths reported to the coroner are sent for a post mortem. However some of these are unnecessary and can be avoided if simple steps are taken by the family beforehand.
There will, of course be circumstances where a post mortem has to be undertaken. The family have the right to object to a post-mortem by informing the coroner. There are also ways to speed up the process on religious grounds.
An alternative to the general post mortem is a non-invasive post mortem by using a CT Scan thus avoiding unnecessary opening up of the body. You can make a request for this by informing the coroner.