This will always be a thorny issue. The distinction between nursing care and social care is becoming increasingly blurred.
The clearest defining criteria that can be applied are wheter or not the premises in question are owned, managed or occupied by the NHS. If the answer is yes, the DoH fire safety policy should be applied.
If the answer is no, the issue becomes less clear. The determining factor is whether the premises is used for the treatment and/or care of NHS patients. One could argue that we are all NHS patients, but the intent of the fire safety policy is to determine whether those occupying the premises are there as a direct result of their NHS treatment or care path.
When this part of the policy was written, the NHS were making increasing use of private hospital provisions and had just started sending some patients abroad for treatement. It was seen reasonable to ensure that the fire safety standards applied to premises traeting such patients should be commensurate with the standard of Firecode.
I'm not sure I've moved this much further forward, but I don't believe the answer is ever going to be Yes or No, more likely to be a Depends!