I didn't know about this and it's quite interesting. But I wonder why it no longer exists this way? Is there a reason why a "for-profit" discontinued a service like this?
EDIT: Seems I found a clue ....
"In 1862 insurance companies told the government that they were unwilling to be responsible for London’s fire protection as the cost of compensation was becoming too high. The government decided that the Metropolitan Board of Works would take control."
It's also worth remembering that fires spread. If the house two doors down is on fire you better hope they and the house next door have insurance (and remembered to pay the bill this month).
You hit the nail on the head which naive interpretations of libertarian isolationism often miss -- unchecked problems spread viz fire, pollution, garbage, disease outbreaks, crime and poverty.
As one's liver combats the effects of pollution in your bloodstream by filtering it, so, as a society, we have developed certain organs to combat the degrading effects of similar sorts of problems.
EDIT: Seems I found a clue ....
"In 1862 insurance companies told the government that they were unwilling to be responsible for London’s fire protection as the cost of compensation was becoming too high. The government decided that the Metropolitan Board of Works would take control."