There are no adds on BBC when consumed in the UK. There are trailers for other BBC content. BBC programs run end to end without stopping. If you consume BBC content via some other medium - e.g. you listen to a BBC podcast via Spotify, you will hear trailers for other BBC content - unless you are outside the UK at the time of listening. If you are outside the UK, the content will be interspersed with and interrupted with adverts, just like on a commercial channel.
I have not tested this, but I imagine if you try and watch BBC TV content via a VPN who's termination point is outside the UK, you will either be denied the content, or will have adverts presented.