Shades of 'Good Times'! The BBC is developing a spin-off from a spin-off to perhaps give them a boost on Wednesday nights. For now it's being referred to as 'Holby Blue' and will focus on the police station that's nearby to the hospital, which is featured in 'Holby City' and its parent series, 'Casualty'.
According to the story I read about this, ITV did something similar with 'The Royal' in 2003, which was spun off from 'Heartbeat'. 'The Royal' was about a small hospital in the village of Aidensfeld in the North York Moors (but only to be found in Toobworld), while 'Heartbeat' was about the police in that area.
The producers of 'Holby Blue' haven't decided yet how much crossover there will be between the various series, but if the past is any indication, then it may be limited to special events like the Christmas specials. (I would imagine there would also have to be at least a few characters from the other two shows to help launch 'Holby City', which is supposedly scheduled to debut on April 30.)
As it stands now, there's not much interaction between 'Holby City' and 'Casualty' as it is, and they take place in the same hospital. (Again, those crossovers mostly occur just during the holidays.)
With the re-invigoration of BBC-America, I wouldn't be surprised if 'Holby Blue' was launched on that network over here, while it was still in its infancy, allowing the American audience to jump in without so much backstory to absorb.