Our house is one of three sharing a drive from the road. The drive
crosses
the front of the houses, so with the width of the drive and parking, I
guess
the opposite fence is about 30 feet from the front of the house. When we
moved in, growing against this fence there was a small silver birch,
perhaps
8-10 feet high from memory. Five years on, it's now got to be heading
for
25-30 feet.

Even at that distance it could be a problem with subsidence in future. You
should also consider that as it is close to the boundary the branches are
already overhanging the adjoining property. As it grows the degree of
overhang, and trespass, will increase. Whilst the current neigbour my be
happy with it a future one may not. As a tree lover I much regret having to
advise you to remove it but that is the prudent thing to do.