I'm not sure that this needs to be a competing answer, but since other people have pressed for it:
Yes, it is perfectly normal in some parts of British society. There are some parts of the independent schools system where this form of address between children and adults is perfectly normal, and indeed the children address one another by surname only.
Draco Malfoy's "Potter", "Weasley", and "Granger" are in fact how all pupils address one another in such schools. Adults, both masters/mistresses and the parents of other pupils, would be "sir" or "miss", or "Mr Weasley" or "Mrs Weasley".
Whether Hogwarts is an independent school, or is state-funded, is a good question (especially as many people's assumption that it is independent seems flatly contradicted by recent pronouncements from the author). But it's another question. ☺ To this question: Yes, what you see is quite normal, and one of the many facets of this particular British schools sector that one can see reflected in the stories.
Don't mistake this for thinking that this is necessarily common across British society as a whole. It is not at all unified in this respect. There are, equally, parts of the British schools system to which these mores seem utterly alien and even appalling. So it can be surprising even to other Brits to hear anecdotes such as:
- One can go through school without ever learning the first names of some of one's fellow pupils. As someone who systematically attempted to learn people's first names, I can report from direct experience that it even went so far as there being people who actually refused to tell me their first names.
- Faced with two pupils sharing the same surname, rather than resort to given names as disambiguators, my Lower Fourth form-master promptly gave both pupils ad-hoc nicknames based upon their (then) appearance, which pretty much stuck with them for the rest of their school lives.
There is also a movement amongst teachers that objects to female teachers being "miss" whilst male teachers are "sir". The twain are not equivalent in status. This is part of a larger linguistic debate over the titles for men and for women, of course. (I rather like James Tiptree Jr's gender-neutral approach to the subject.)
Equally, do not mistake this for being something that is strictly peculiar to independent schools. It is just far more common and far more pronounced, to the inclusion of pupils, there. There are some state-funded schools which adopt similar codes to lesser or greater extent. To give two current examples:
- Addressing adults in this manner is actually in rule #1 of the School Rules for the Queen's School, a state-funded school in Hertfordshire, today:
Be polite, kind and helpful to teachers, support staff, visitors and other students, regardless of their age, colour, religion, race, language, sexuality or background. Address male staff as “Sir” or “Mr” with their surname and female staff as Ma’am’, “Mrs” or “Miss” with their surname.
- It is in the first rule of the School Rules for St Dunstan's School, an Academy Converter in Somerset, today:
Behave politely and sensibly at all times. Show respect for other people and their property. Female staff should be addressed as Mrs, Miss with the surname. Male staff as ‘Sir’ or Mr with the surname.
Yes, being required to address teachers in this way does bleed over into addressing all adults, in and out of school, in this way. In the opinions of some, it is intended to.
If you want to read even further about this across society as a whole, then you can do worse than to start with the publications of the Society for Name Studies in Britain (president: Peter McClure, Honorary Professor within the Institute for Name-Studies, University of Nottingham).