The highway code is not the law. There is a provision under the Road Traffic Act for fixed penalties to be issued to hgvs parked on the verge or footpath, but not cars.
The offence would have to be unnecessary obstruction, or wilful obstruction.
The problem is the driver could argue that is was necessary to ensure the free flow of traffic and / or there was no intention to wilfully obstruct.
I believe that if the road is not wide enough to allow traffic to flow freely with vehicles parked both sides, there should be no parking on one or both sides.
I do agree, though, that drivers who do park in this way are a menace.