I have to do this a lot, one of my least favourite jobs...

From what I have seen, yes, it WILL eventually damage your roof, by getting between the tiles and, as Sasha said, the thickening of the stems then forces the tiles apart.

In your situation, I'd pay a window cleaner to go up a ladder and cut it just below the gutters, taking care to cut every stem. I'd then cut every stem myself, at a lower level, wait until the leaves go brown then lever off one stem at a time - if you pull them downwards and outwards, you can often get great long streamers of them off (hence the "cut at the top" advice, to avoid damaging the roof/gutters).

Then you can, if necessary, pay a roofing company to go up and check the roof, removing the dying ivy that's up there, and replacing any damaged tiles/gutters. Hopefully you will have caught it before there's much damage.

NB if you live in a bungalow, you can do most of this yourself!!

The urban myth about ivy damaging walls relates to the days of soft lime mortar: modern mortar is pretty impregnable BUT in my opinion I'd take the ivy right down anyway as it holds dampness and insects against the bricks.

Good luck with the job.

Oh, and yes, I'd also dig the root out and spray any tiny re-growth with glyphosate-based weedkiller ie Round-up.

Rachel