I am an ex grave digger, we always removed the whole of the memorial prior to digging a grave, that was essential!!!
A double depth grave was 6ft deep allowing for two coffins to be buried on top of each other, the second grave being 4ft deep being dug on top of the first, we often came across the first coffin whilst digging, we would just ensure it was covered so as not to upset mourners and to keep flies smells etc at bay. Side by side graves are sometimes allowed but this is usually for family members other than husband and wife. Sometimes graves are made to look deeper by building the soil level up around the grave to give the impression of depth, this is done where the first coffin wasn't buried to the correct level, we would then cover the coffin with concrete to prevent the coffin being unearthed by animals, not likely but possible!!
It is actually illegal to remove the coffin once it has been placed below ground level, only permission from the home office could permit this!!
I had to remove coffins and remains on occasions, sometimes with permission and a few times without permission!!