This is an interesting thread. Differences in culture, law, geography, etc., as well as what may simply be differences in terminology as well.
My main objection was the term "fine". To my experience, a fine is a criminal penalty, and thus could only be enacted by law and enforced by a government entity. Such a law would have to be duly created by proper procedures, and would need to be enforced under proper criminal procedures, due process, etc.
On the other hand, if these are not fines, but actually "fees" (in US terminology), then this would all be a civil matter, and subject to civil law.
In the end, the common practice in the US, of having violating cars towed and impounded by private towing companies ends up being similar in effect. And this practice is common, and accepted.
Here in the US, you can have a car towed if it is blocking your driveway because blocking a driveway is illegal. But if it's simply in front of your house, legally parked on a public road or street, then unless it's there for a long time and can be deemed to have been abandoned, that's not something you can prevent.
It's also interesting to read about price-shopping, fences, etc., being somewhat different between the US and UK.
Fun thread, everyone!