If the deceased left a valid will appointing executors then possession of the body passes to them. In all other cases the next of kin will take possession.
Executors or next of kin will almost always want to carry out the wishes of the deceased unless it is not practical to do so. The will should be checked for any expression of wishes.
Sometimes problems will materialise if the deceased wishes were clear but someone objects. In this case the executors are placed in a difficult position and need to consider all the circumstances and the reason for the objection.
It is worth noting that surprisingly the authority of the executors even overrides any wishes of the surviving spouse or civil partner. Clearly this is a sensitive matter and executors should only override the wishes of the surviving spouse or civil partner if there are compelling reasons to do so.