In an ideal world you'd have a separate aerial for every TV channel which you watched. That's because, for optimal reception, the lengths of the elements should be exactly matched to frequency of the channel you want to watch. Obviously that's not practical, so all aerials are 'a bit of a compromise' with the elements only being roughly matched to the frequency of any particular channel. That means that, inevitably, any given aerial will be better at receiving some channels than others.
If you were in a strong signal area, with a good quality aerial, it wouldn't matter that your aerial is slightly better at picking up some channels than others but, clearly, your particular aerial isn't good enough for receiving the group of BBC channels.
When the digital TV was first planned it was expected that around one third of viewers would need to upgrade their aerial systems. (i.e. both the aerial and, just as important, the cable). It's turned out that far fewer people actually need to do so, but it's still unsurprising when certain people experience problems due to insufficient signal strength.
Since you're receiving other channels, you might be able to resolve the problem by simply using a cheap signal booster. If not, it's time to upgrade your aerial and cabling.
Chris