As a general idea, many believe that a tree's roots roughly match the canopy, so, if the canopy is overhanging your neighbour's fence, then the roots may well also be in the vicinity too. With regard to possible action, my view on this is very much along the lines of "if it ain't broke - don't fix it".
A lot depends upon soil type and the proximity of other plants. If you have never had problems with soil movements, subsidence / heave, then there shouldn't be an issue. Prune off the bits of the canopy that overhang the fence, and, if you don't like the comforting sounds of the ends of the branches touching the windows on a cold stormy autumnal evening then just cut off the bits closest to the house as well.
If it were mine, I'd leave well alone and enjoy the majestic beauty of a magnificent tree.
Paul
After some consideration, I think it's the depth of the roots that's the issue. Since Googling, I've read, rather alarmingly, that the horizontal spread of the roots is the same as the height of the tree. I haven't had problems with subsidence, etc. yet, but waiting until the problem starts is probably leaving things a bit late. It is definitely too wide for the garden, and rather than me hacking off bits as they smack me in the face, it needs addressing by somebody who knows how to prune it whilst maintaining some shape. I'm inclined to ask a tree surgeon for advice and an estimate. Hopefully, the roots are deep enough not to be problematic. The only other plant in the vicinity is the lawn (complete with various weeds, and an annual crop of bluebells.)
