Depending on the kind of eucalypt (there are hundreds) and the soil type,rainfall etc, you'll get quite different root spread in different scenarios. They do generally (in my experience) have very deep tap roots, though again, this may be related to soil conditions and rainfall (most I've seen have been in Australia). In Australia, you'll find gums along rivers which flow only in the wet season - the rest of the time the trees get their water supply via their tap roots from the water table, which is often very deep. (Hence the reason why if you see a line of trees along a gully and need water, its as good a place as any to head towards.)
Their roots are tough and do pull up foundations, by expanding with growth. If you cut roots off along a fence line (just one fence line) there's probably little chance it would keel over (due to not just a root spread, but a deep, thick tap root accompanied by roots on the other sides). I've pushed over maybe 30 or so dead gums in my time (with a tractor - the trees had been poisoned by someone else a long time before), and, with the minor roots gone, the main root ball, with the thick roots, doesn't usually exceed 5 m in diameter for a tree perhaps 30 metres high. 20 foot for a gum tree, dependent on species (snow gums I think are generally quite small) is not high. Some gums grow to over 100metres. Most species are probably in the vicinity of 20-30 metres.
Also, along with the tap root, they tend to be pliable in the weather - many forests will stand up to (shredded and split often, admittedly) category 4-5 cyclones. They get beaten around a lot, but even in such weather a significant portion survives. So for most UK weather even a root 'trained' gum shouldn't present too much of a problem.
But if you're looking for a way to raise the subject again with your neighbours in a tactful way, point out the probable damage the tree is probably causing to *their* foundations, and direct them to experts on subsidence - there seems to be plenty of examples even in the UK of eucalypts causing subsidence problems.
cheers,