I have Comcast, the Digital Starter package, that comes with OnDemand (as well as a Comcast DVR with TiVo) so I do not get BBCA buuut I've still been able to watch the episodes of Doctor Who listed as available on OnDemand (HD versions), including the newest ones.
Altho it has now been more than a day since the 3rd ep of the 6th season, & it is not available yet/ still has not shown up (which is how I found this question, lol searching to see who else hasn't found it posted yet) but I think that is simply a general OnDemand issue, not package-specific, heh.
The only OnDemand programs I've really ever had trouble viewing were movies from premium movie channels (which I also do not have). Hope this helps!! XD