if your case is straightforward and well-documented, there shouldn't be much of a problem -- as far as I can tell. the quick reply from the Home Office suggests there's not much of a back-log and, as you can see, I got my letter in just a few days over a month. There have been others on this board who have had letters back in a similar time frame.
It's not worth ringing the registrar, because they won't have the information till after the application is approved; once you get the approval letter from the Home Office, the registrar may be able to help you find the quickest way to get yourself to a ceremony (the free group ceremony or a private one for a fee, for example). Note: the Home Office letter instructs you *not* to ring the registrar, but just to wait for them to send you an invitation to the ceremony. Actually, there's no real reason you cannot ring them -- but I suspect they tell you not to for two purposes: (1) the registrar may not actually know about your application yet, if the info hasn't had time to arrive from the Home Office and (2) some councils will be servicing a large immigrant population and may be flooded with calls already; they don't need more and they'll get irritable. In my case, since I don't live in an area with many immigrants, my registrar was lovely when I rang -- but, for reason (1), she didn't have much advice to give yet -- not late last friday!
As for ringing the Home Office, I think there's not much point -- and there are a couple of former Home Office Caseworkers on this board who have said the same thing. Your application will be in a Big Pile right now -- and, although ringing up won't hurt your chances, it won't help either, because you'll just have to wait your turn like everyone else.
As I said, if your application is straightforward and doesn't require too many checks, you probably won't have toooooo long to wait! ;)