Think the World Service has only “officially” been available in the UK since the introduction of DAB too (though you could pick it up on shortwave and AM broadcasts aimed at Europe, of course).
In terms of national, 24/7, officially aimed at the UK reception, then yes.
However you're forgetting the many years it's been carried on R4 overnight and, as deejay said, some BBC local radio stations used to take where others took 5 Live.
It was - if not still is - the case that R4 overnight, UK DAB, Europe (although no longer on 648kHz MW) at times carry a different mix of programmes. Not opt outs as such, different schedules. As just about every programme has fixed start and end times (and numerous other 'posts' each hour) then it's not too difficult to provide a custom schedule for any area / rebroadcaster that wants it.
When I worked there, if you were at home it made it a bit of a game knowing whether you'd be able to hear a particular programme you'd normally be part of!