As pointed out here, Michael Swan, Practical English Usage indicates:
Both verbs can be used in British English to talk about obligation. (In American English, have to is the normal form.) British English often makes a distinction as follows.
Must is used mostly to talk about the feelings and wishes of the speaker and hearer for example, to give or ask for orders.
Have (got) to is used mostly to talk about obligations that come from "outside" for example from laws, regulations, agreements and other people's orders.
Also, "Must you" is much more formal and as such rarely heard in speech, esp in AmE {SPOK at COCA} these days.
E.g. at COCA (CORPUS OF CONTEMPORARY AMERICAN ENGLISH)
. DO YOU HAVE TO
in [SPOK]
52 hits
. MUST YOU
in [SPOK]
0 hits
I am using the "." as part of the query to look only for sentence starts.
At the BNC (BRITISH NATIONAL CORPUS):
. must you
http://bnc.bl.uk/saraWeb.php?qy=.+must+you&mysubmit=Go
3 results
[At BNC
. do you have to
times me out and I'm talking to the Webmaster about it:-)]
For more information on usage, check this grammar forum discussion: