In a workplace, the employer carries the general risk assessment duty and is normally the responsible person for fire as well. Where nobody is employed on the premises, fire responsibility follows control: the person managing the building or, failing that, the owner. The same logic decides the equivalent dutyholder roles in Scotland and Northern Ireland, so the analysis travels across the UK.
In residential blocks the usual candidates are the freeholder, a residents' management company, a right to manage company, or the managing agent whose contract hands them control of the common parts. More than one of them can hold duties at the same time, which is why who is the responsible person in a fire risk assessment is worth settling before any work is commissioned. Leaseholders and residents, by contrast, are almost never the duty holder for the shared areas, however closely they follow how the block is run.