I know the Christmas special was aired quite late, and I remember a few years ago when they made a Vuvuzela joke and instantly made it clear that they were on a 6-12 month delay.
The day after thing with Dr. Who is because it's airing at the same local time in the US as it does in the UK I believe, which is perfectly reasonable to me, i'd rather not have to watch it at something like 5am :)
What shows are you referring to? (Downton Abbey is not BBC, its aried on ITV in the UK.)