I received an 'informal' offer as it's my home dept, after around six weeks, the letter didn't come for another three or four though.
If you do need to know urgently I suggest you tell them tho. It won't necessarily make any difference -- I had an offer of a partial scholarship from LSE but wanted to go to Oxf; had to give my response on the scholarship rapidly, but Oxf didn't oblige in telling me whether I had an offer for another three months. Very stressful times!