I like your approach Kurnal and to be honest, I would agree with that as a method I would use.
For me, the priority would be to get rid of the heat detectors in room and have smoke detectors, and before I get ripped to bits, I know all ablout the false alarm issue, but I value the life of an occupant more than the inconvenience of a false alarm.
There are of course, interim measures such as single point detectors where cost is a huge problem.
Current cases have referred to CLG guidance which clearly identifies the level of detection required.
As for the doors, I would advise an audit of all doors and a priority list drawn up (like Kurnals). If a responsible person has a documented actionplan which acknowledges the deficiencies and a course of action to rectify them, then I would accept that as it does demonstrate diligence.
Further inspections would be needed to check progress, but that is a monitoring process, not an enforcement notice issue.
On any audit and inspection, I recommend that doors are brought to current standards perhaps as a rolling program. Only new doors which are installed as a set are, as I understand it, capable of meeting the standard of BS476. (you can all shoot me if that's not right!!)