It seems a bit strange that when you knock they refuse to answer the door - after all them boxing you in is so that they can get the space when you move your car.
Id keep walking and leave your car parked in the spot for days at a time, this will frustrate them more than anything else.
Yes, this is what I don't understand. Surely, they must 'give in' at some point and move, otherwise there's no way that OP can ever move her car out of what they believe is 'their' space - unless the cars in front or behind move, I suppose.
I'd be inclined to contact the fire brigade (non-emergency number) direct and tell them you're worried about fire safety in your road. You could even play a bit 'simple'. Ask them to come out and advise whether they would be able to find a way past the car that very frequently parks there (no need to say why they park there).
Fire brigades in general seem to (very wisely) invest a lot of time in measures in the community to educate and advise so as to reduce or mitigate fires in the first place, to prevent the likelihood of tragic losses of life and homes.
Of course, they will confirm that they cannot safely get past. Their normal course of action, if necessary, would be to bulldoze the car out of the way with the fire engine - which invariably writes the car off (with no hope of an insurance pay-out to the owner), but naturally also slows down the engine in getting to the fire.
I'm sure that, if they report the car to the police, they would take it very seriously. Of course, the police/fire brigade may go and 'strongly talk to' the neighbour themselves. Either way, it's somebody 'official' dealing with them and stopping/punishing their dangerous behaviour and not you having to endanger yourself.
How embarrassing for the stupid PA neighbour to have to be officially informed/cautioned that, if you park blocking the road, it blocks the road!