A report in The Guardian today reveals that there will be a preview screening of episode 1 of Season 7 during the Edinburgh International Television Festival.
The Festival runs between 23-25 August 2012 and the article states:
The Doctor Who showrunner, Moffat, will give a masterclass on BBC1's Sherlock, along with his co-creator, Mark Gatiss, and the producer, Sue Vertue, and there will be an exclusive preview screening of the first episode of the next series of Doctor Who.
Obviously, this doesn't necessarily mean that Season 7 will start airing the following week. Last year, the preview screening at the BFI for "Let's Kill Hitler" was on 15 August 2011 and it subsequently aired on BBC1 on 27 August 2011.
Steven Moffat has previously stated that Season 7 would straddle Christmas - leading many to believe that November was a likely start date (especially with the Christmas episode being mooted as episode 6). However, with this preview screening in late August, it seems that a September start date is now favourite...