There's a couple of reason they do this:
1. Many programmes are purchased now and in a format suitable only for commercial stations, without BBC "adverts" between them you wouldn't have a normal schedule, it'd all be finishing at random times i.e. 7:43pm, next program finishing at 8:12pm. It'd be a nightmare. In most US stations 25% of the viewing time at peak hours is adverts, not shows.
As was already pointed out once in this post, that's not the case.
The show is re-edited for overseas broadcast when it's sold.
Two reasons for this:
One is that BBC is a PSB which is funded by the license fee, it also has a Trust setup to monitor it. For the BBC to be making shows with the intention of purely selling them on and editing them as such would go completely against it's remit and most likely also breaches Offcom terms.
Secondly, shows being sold on comes under BBC Worldwide which is the commercial sector of the organization. Here is where they will actually adapt a show for other territories, and let's face it, it's not difficult to fit in an ad break.
Just as an example, we could use Top Gear on Dave. That has ad breaks, but they didn't create the original show around them did they, or edit as such? They've just added ad breaks at natural places to do so.
Finally, I'm struggling to see what BBC ad breaks are being referred to here now. The ones between shows advertising other BBC shows? As those have existed for as long as I can remember.
If you mean specifically during a show, can you give some examples? As I watch BBC channels a lot and have never seen one.