In this case, you need to contact the local department of human anatomy to see if they are willing to accept the body, and if not, if there is anywhere else willing to accept the donation.
See details on the Human Tissue Authority website.
The hospital or doctor will normally help arrange this.
How long the body is kept
The body is normally kept for up to three years and then burial / cremation arrangements discussed with the family / representative of the deceased.
Registering the death
Please note that the death will still need to be registered in the usual way.