Funerals can be what you want them to be.
A Funeral Celebrant can be employed in a crematorium, or can conduct a private ceremony at another place of your choosing. It is normal for the body and the ceremony to be in the same place, as in a crematorium.
However, the ceremony can take place at a different time and location if you wish. The ceremony could take place in a village hall, your back garden, or a local beauty spot. Perhaps somewhere that has a special significance. You may need permission to hold the ceremony in certain places, however funerals can be as public or as private as you wish.