If it obstructs the entire pavement, call the police, it's a problem for them.
I'd ban all and any parking on pavements (and anywhere that isn't a road and driveway) tomorrow. There's no excuse and it's simply unacceptable.
Unfortunately, it isn't (other than in London). Police can only do something if they actually see the car being driven onto the pavement (in which case there is a relevant offence under the Road Traffic Act which can be used).
Seriously, I didn't make it up, I copied and pasted it from Surrey Police (who aren't in London). And more so, when I dibbed the driver who parked on the corner opposite my house, the police spoke to the registered owner (him) and when he ignored them, issued him a fine and three points. I know this because I made them a cup of tea and they told me.
I suspect it was “leaving a vehicle in a dangerous place” rather than (or in addition to) wilful or unreasonable obstruction.
It's what they told me and the car disappeared in a puff of grump. There's double-yellows now and they seem to have stopped the problem. In my experience, if there's a space left anywhere, modern
Homo driveverywhericus will park a car on it. We were walking through the back end of Dorking at the weekend, and there's a small estate, as usual, all the front drives have been converted into crappy driveways and still, all the green verges along the road, verges that might have added some colour and life the roads, were covered by (and churned up) by cars. It's something we have sleepwalked into. Front gardens shouldn't be driveways. Green spaces shouldn't be parking spaces. It's a gross social failure.
And yeah, when they turn their nice front gardens into a slab of greasy concrete, it's still sometimes not big enough for an entire car, plus they get another couple of cars, which don't fit in the space, so they dump the third across the pavement at the end of their drive, the bit of parking that was previously available to anyone, but now annexed, along with the pavement.