Trees and their proximity can have a drastic effect on a building depending on type, and size of tree! Not only on the obvious obstruction of light but, how they draw moisture out of soils and cause buildings to move.
But the answer is not to just cut down the tree! This can have a devastating effect as the ground goes into shock and is unable to cope with the fact that the tree is no longer there drawing the water out of the soil!
If you are in an area of predominantly clay soil this can result in heave occurring where the ground literally swells which can create far more drastic building movement. Tree removal in such locations must be a managed process usually with the help of a qualified arboriculturist.