You pay more in higher-risk circumstances, yes: high risk events generally seem to pay for it, and of course more valuable properties pay higher taxes too. Just as smokers pay considerably more toward the NHS than non-smokers.
My building's high risk - big gas-powered generators in the basement - and we do indeed pay a substantial amount extra to the fire brigade each year because of it. Bigger properties also tend to pay higher taxes generally, to fund such services, as well as being held to higher standards regarding fire alarms, extinguishers etc.And you haven't had a house fire, so you shouldn't be expected to contribute to the fire brigade either.
As for price: yes, the NHS is cheap. It's also very nearly killed me once due to inadequate staffing (or rather, politically skewed staffing: instead of a proper hospital, they were fighting to keep a "cottage hospital" open with no actual doctors in, hence no properly trained staff when complications occurred). I'd rather have an expensive system that doesn't kill me, thanks.