If the flats cannot be considered safe for a stay put policy (eg 1 hour fire resisting construction, lobbies between any room and the staircase, short travel distance, ventilation in corridors and lobbies, no ancillary accommodation opening into staircases) then a full evacuation strategy is necessary in the event of a fire anywhere in the building- in other flats or in common areas (if you could consider that possible travelling down a smoke affected stair from 10 floors up and if you dream that folks may take any notice of the alarm at all?

).
The flats are domestic property but the persons in the flats are relevant persons who would be at risk in case of fire in any other flat or in the common areas.
So in that case a full alarm system would extend to all parts of all flats probably with smoke detection in stairs, heat detection in flat lobbies, sounder from the main system in each flat with 75db in the bedrooms, and a seperate smoke alarm in each flat.
You could educate the residents as to the reason for the system, try and persuade them to co-operate, minimise the risk in common areas and enforce this.
Can it work- not on your life.
Would people respond to the alarm? No way.
But that would be their decision. The RP would have done all he reasonably could.
But what else could you realistically do to improve standards in an existing building of the type described?
Sprinklers or water mist would be ideal but unlikely to be acceptable from the cost and disruption points of view.