The fire itself may be evidence of a crime, or evidence of other crimes may be damaged or destroyed by fire, your objections to the fire being controlled may have any number of motivations, all of which could be disputed after the immediate event.
The fire fighter does not have the luxury of time to set up a debating group to discuss the merits of wehter or not to tackle a particular incident.
The overriding presumption is surely to act on the assumption that there is a risk to public safety unless its immediately apparent there is no such risk, which would need the ‘once over’ by a trained professional such as a firefighter.
Immediately apparent would mean just that, quickly obvious, if in fact there was no real risk, but it was not obvious there was no real risk, then the firefighter would still be in the clear.
You could ask the firefighters not to enter your premises but I would assume that they would wish to make some sort of assessment, if the result of their assessment was that there were some risk, to persons, property or environment then you would not be able to legally stop them.
In that situation, they would most likely take a look, decide the risks were nil and would withdraw, although they might keep someone around to monitor things.
They might also look to see if you had taken sensible precautions, they would (in Europe and especially UK) send in a Fire Authority inspector who would investigate wether you had carried out the necessary evaluation of risk.
It is possible that the risk was negligable but you might be prosecuted for not making a ‘suitable and sufficient’ risk assessment.
In most incidents, there is a person available, such as a senior supervisor, who would be able to lock the site down until other investigators arrived, and the lock down would happen if there were any suspicion of some crime.
In the UK, fire authorities have their own investigators who have the powers of constables, and actually have some extra powers, such as the right to enter premises without a warrant, usually accompanied by a constable who is under the inspectors orders.
Such an inspector could certainly sieze any evidence relating to criminal fire damage, other evidence would be reported to police investigators.
Setting traps, or having your premises as being unsafe to enter, by way of your African Lion traps would be a criminal offence, I could quote the actual wording and Act of Parliament exactly on this issue, it would come under ‘Persons in Control of Premises’ which is a subsection of the Health And Safety At Work Act 1974(HASAWA)