The Manual of Drill and Ceremonial has a chapter on funerals and religious services. For the funeral, it lays out exactly what is authorized according to the rank of the deceased. It does have a short section on cremation, but basically it is all built on the traditional coffin, with a service in the church or the chapel with the coffin present.
But you can always scale down from the full monty, if you wish. If the family wants to have a more simple service, it is very easy to scale down to meet the family's wishes, and in fact it is written into the manual that the family's wishes will be respected as much as possible.