Is using the last name of a person without a title an accepted way of addressing?

I always heard people use Mr/Mrs/Miss/Ms before people's names and that is how, I thought, it was done until I watched one of those Harry Potter films in which Malfoy (Sr) addresses Albus Dumbledore as just Dumbledore. I noticed later that even Rubeus Hagrid was addressed as only Hagrid. (I have actually read all the seven Harry Potter books but it never occured to me while reading.)

Is this way of addressing people common and considered polite?

A hundred years ago, even in the US, men used last-name-only in addressing:

• Those of either sex who were distinctly inferior, socially or professionally
• Male equals with whom one was on familiar (but not necessarily intimate) terms
• Boys and young men to whom one stood in a professionally superior but socially equal relationship

They added the title in addressing:

• Social and professional superiors
• Social or professional inferiors of either sex entitled, by virtue of age or status, to a distinct mark of respect
• Male equals with whom one was not on familiar terms
• All women who were not distinctly inferior

One addressed by the first-name-only

• those of either sex with whom one was on affectionately intimate terms.
• children
• contemptibly remote inferiors

Women followed the same rules, with the sexes reversed, except that they addressed women equals by last-name-only only in (then rare) professional or school contexts, and the first-name "intimacy/familiarity" line seems to have been drawn a bit less stringently.

In the US, over the course of the last century, almost all uses have been swallowed up by first-name-only, except where tradition or professional discipline enforces use of titles to eminent superiors. I believe the same is coming-to-be in Great Britain, too; but you must consult a native speaker on that.

The use at Hogwarts in the Potter books reflects very traditional public-school practice, which spiceyokooko addresses in more detail in the Comments.

EDIT:
I am moved to add, in light of the discussion in the comments, that it would be gravely discourteous (not to mention deleterious to discipline) to omit a deserved title when addressing anyone in the presence of his or her subordinates.

This is common in high-end Private schools in the USA (oddly the equivalent in the UK are often referred to there as "public schools"). When I switched from a public school to a private one, this was one of the first things I noticed. My guess is that addressing by family name only is a subtle way of reminding the (typically upper-class) students that they are representing their family there. That's just my theory though; all one can say for sure is that it's a cultural thing. I've never observed it being the common form of address anywhere else in the USA.

Presumably (based on the evidence from the books) UK "public schools" share this cultural feature. Hogwarts is meant to be special public school for magic users, so they'd need to address each other that way for verisimilitude.