The comparison with the medical profession is not relevant. There is no enforcement role.
Following this line of logic you could argue that a soldier keeping the peace in one of the worlds trouble spots is entitled to go and fight for the enemy when off duty.
I would not have a particular problem with fire safety officers doing a bit on the side if it is open and up front, if the fire authority is aware of it and they do not enforce standards in the premises that they cover as a private consultant. But most who do this work do it in a surrepticious and underhand way without the fire employers knowledge and so may be gamekeeper and poacher at the same time. This is wide open to corruption, just like those notorious gangland cases in which police officers were given an inducement to turn a blind eye.
For this reason most enforcement officers are required by law to declare all inducements offered or hospitality received and record it officially in a document that is accountable and open to public scrutiny. I suggest that offering a service for a fee is exactly such an inducement that should be recorded.
So I would say, to do it right and protect yourself, apply for permission, provide a list of your clients to the fire authority, declare vested interests, keep your business and enforcement roles completely seperate- Never never tout for business whilst wearing your uniform or as part of your enforcement duties.
If theres one thing that does frustrate me its that poor advice given by a recruit firefighter on the trucks with no experience or knowlege of fire safety enforcement or standards has 100% more credibility with the public than good advice from an independent consultant with 35 years in the industry but wearing a suit.