I have been tuning in recently to Absolute 80s on Digital Radio in London. There is a playlist which does repeat, but it has some varied announcements, which are interspersed in the back to back music. They are also available on Sky and online at
It also seems that at present Big L on 1395 features a lot of back to back music. I am a bit confused by the many references to KBC Radio, which of course has been broadcasting Wolfman Jack on shortwave for some time now.
I have said before that I do consider radio stations which have music back to back, as good entertainment, as long as they have some form of appeal to them. Some internet stations rarely do seem to have more than back to back music, which can be rather tiring. In the sixties we did not have any stations that played music back to back, possibly with the exception of Workers Playtime, and then of course Britain Radio Offshore with their carousel unit. Of course we had pirate radio stations offshore with test transmissions full of music. Caroline was rather fond of playing out Beatles tracks.