The insurance company firefighting teams, though the name sounds like a business, were actually the most experienced and reliable force within the 19th-century London fire emergency response system.
In those times, there was far from being any government-established firefighting system. Even the so-called London Fire Department was actually funded by multiple insurance companies, specifically to protect insured buildings from fire damage in this private sector.
They were not under government control, but the binding power of insurance contracts over them was evidently much greater than Whitehall's administrative orders over Scotland Yard.
These professional firefighting teams were exceedingly loyal to the insured properties, and once these guys equipped with various firefighting apparatus were deployed, it meant that a truly professional team had entered the battle.
