The first part of the fire safety ‘lifecycle’ for any premises is when it is being constructed or altered; in respect of fire safety this work is controlled under the relevant Building Regulations, which can already be enforced by the private sector (Approved Inspectors). My initial thoughts were therefore “why should the enforcement of the legislation that deals with the occupied premises be any different”?
I think it is different, though, because the nature of the legislation is that it relies upon the enforcers operating targeted, risk-based inspection of all ‘at risk’ premises. I would suggest that there could only ever be a single entity within any geographical area that could be accountable for developing & maintaining such an inspection regime (discounting for the moment ‘special’ premises such as nuclear power stations etc). It would be hard to see how this could be anyone else than the relevant fire authority (FA).
Nothing to stop the FA from employing civvies to do this work, or even to stop them outsourcing it to a private company, but they would need to retain the ultimate accountability for whether it’s done right or not. In the case of outsourcing if they draw up the contracts right, procure competently & enforce the contracts rigidly, I can’t see why (in concept) this wouldn’t work. The private companies might also be able to do it cheaper not because private sector employees are necessarily paid less, but the private sector’s overheads (pensions etc) are often much cheaper, which means they might be able to pay their staff more & still turn a profit.
Note that I said "if they draw up the contracts right, procure competently & enforce the contracts rigidly, I can’t see why (in concept) this wouldn’t work..." I would observe that the ability of the public sector to achieve all three of these might not be entirely reliable!