Is there a risk that the tree will fall over, and should I have it 'topped'? It looks healthy enough, with no apparent root movement; but if it did go over, it would hit our neighbor's bungalow.
50 Foot Eucalyptus Tree
Hopefully, this article will help: https://www.gardeningknowhow.com/ornamental/trees/eucalyptus/eucalyptus-pruning.htm
Knowing how much damage "topping" a tree can cause, I don't recommend that pruning technique.
pruning a tree or shaping it is always good but if the tree is balanced there is no cause for concern.