[MikeHardman]

I wonder if anybody can tell me about this tree.

It looks generally like a Ficus benjamina, but the leaves are a little different and (key point) it is prone to putting down aerial roots which coalesce with the trunk, thereby expanding it.
It is because of that latter characteristic that I am considering using it to help stabilize a steep soil bank. Specifically, I'm hoping that by planting so that the trunk is laid back close to the slope, it will root into the slope in multiple places. In so doing, it should be less prone to leaning over as/if the slope gradually moves. The downside with this theory is that if the trunks become wall-like, they will channel the storm water straight down the slope, exacerbating gulleying. But the experiment is just on paper at the moment, so it can easily be changed.

Ficus microcarpa is my best guess.

[pamela]

I think its Ficus nitida. I have 2 and they do have aerial roots.  But I can hardly see the leaves on your picture.  The leaves on F. nitida are darker and more leathery than F. benjamina

[MikeHardman]

Thanks Pamela.

Sorry my photo doesn't show the leaves usefully, but you are right in your description.

Ficus nitida is a synonym of F. microcarpa (and F. retusa) (http://fichas.infojardin.com/arboles/ficus-microcarpa-laurel-indias-ficus-nitida.htm).
So I think we are converging on that as an answer.

Several web pages comment on it being highly invasive, especially if a suitable pollinating wasp is in the area (whence numerous seedlings). I don't know if such wasps exist in Cyprus, but I shall have to pay closer attention when I see one of these trees in future - looking for seedlings.
It can also be damaging to man-made structures, so wise to keep it away from buildings, pavements, drives, drains, etc.