There is a fair bit of 'contract' law and case law surrounding this issue. Clearly it is a conflict of interest to work as a fire officer in an area where you might do fire risk assessments (and I wonder about issues such as the premises being in one part of the country, however, the 'body corporate' being elsewhere??) as it is not right to be 'both sides of the fence'. As yet, however, I understand that this particular situation is untested in law.
That being said, there is case law suggesting that it is not lawful for an employer to stop an employee doing work, when the work is not being offered by the employer. A very interesting case arose a few years ago in Nottingham (Nottingham Uni I think). In that case a research scientist, employed by the Uni, did research for someone else and got paid. He then got sacked. But the court said: because the research work done privately was different to his work at the Uni - and the Uni was not offereing the same research facilities to any potential clients - this was unfair dismissal. And the Uni had to pay compensation.
If a Fire Authority offered a fire risk assessment service therefore - any firefighter/officer employed by that authority would be in serious breach of contract for working part-time doing fire risk assessments - due to conflict of interest as they would be 'poaching' clients. That is the main rule that's been established for other industries. I do not believe that this is the case here though.
By the way, I've been following this topic whilst supporting one of my officers who took out a grievance against our fire authority who refused permission to do such work. He lost! And although he probably had a good case for the courts, we considered it too risky to risk his job or cash as the FBU were not happy to support him.