It's complicated, Mrrzzy, complicated not least by the fact that substantive , acting, and brevet ranks are none of them the same thing! But, essentially, signing yourself by rank is an officer thing. A non-com might tell you what their rank was (or is), but I don't recall seeing any particular examples where they make a particular point of it, if you see what I mean.

If you don't, since we're talking about signing... errrr… writing abo... Oh, never mind! ;-) Assume a letter to the local newspaper. In the UK, I may be wrong, but generally speaking a serving officer shouldn't do any such thing unless he is very definitely doing it an official capacity. But a retired officer might sign himself "Col. Fred Bloggs (Ret)" to make it very clear that he IS retired. A sergeant might tell you in the course of his letter that he was a sergeant to lend weight to whatever point he wants to make. But he wouldn't usually sign his rank as well.

That's my general impression, anyway. I have never served, I hasten to add!