Depends on the construction of the building,- if all floors and walls are 1 hour fire resisting, if all flats have a protected entrance hall, if all flats have a half hour door to the entrance, if travel distance across the landing to each flat is no more than 4.5m and theres no other fire risk in the staircase then mains powered smoke alarms in each flat to LD3 spec of BS5839 part 6 would suffice and no common alarm in the staircase.
The 4.5m could increase to 7.5m if there is ventilation in the stair
But if these conditions are not met its essentially classed as a HMO and the fire service may then rightly require more than this under the RRO and it may be subject to licensing under the housing act.
Take a look at Approved document B available for free download - google for planning portal.