The tree is a eucalyptus, really tall - around 60ft. About 3-4 metres from the back of the house. The garden slopes immediately very steeply downwards from the back of the house so presumably there are a lot of roots deep under the house. And it’s clay soil. It’s a 1930s house with those shallow foundations that just sit on the soil as seemed to be the way they built houses then.
Is it a bad idea to remove this tree? What effects could removal have on the house?