I suggest you get an arboriculturist to inspect the tree. Some pathogenic fungi can weaken a tree significantly with relatively little sign from the outside. A sign that internal decay may have begun is large limbs having broken off (though that can also occur with sudden water stress). And if the tree overhangs the house, that should be a concern - as well as the tree toppling in its entirety. Also note that, even if the tree were to fall away from the house, the heave of the root plate could still damage the house, depending on proximity.
If the tree has to come down (a shame, I know; and beech are one of my favourite trees), a good tree surgeon (perhaps recommended by the arboriculturist) should be able to manage the process to minimize risk to the house and grounds.
What to do with the felled timber?
- I would hope you could sell it, though that would depend on the degree and type of the decay, and the local supply/demand for beech.