What action can the council take?
Again, do you have an example of that regulation being used in the successful prosecution of the driver who left his/her car parked in such a way as to prevent access
to someone's empty driveway?
The local council is the Highway Authority (but the Highway Authority may not always be the council), and they have a duty to maintain highways to certain standards - which includes enforcing the the public's right to use the highway (roads and paths) and their "enjoyment" of the highways. This includes enforcement action against nuisance, obstructions, danger and stopping/blocking.
The council has the powers to enforce regulations under the Highways Act 1980, and some other associated legislation. They do this via the magistrates court
Now the Police have there powers in various other legislation which is mainly of a Road/Traffic nature and is more to do with the vehicles and their use of the highway rather than the free passage and maintenance of the highway which the is the responsibility of the Highway Authority.
The two areas of responsibility can blur (use/passage), and this can lead to confusion of who enforces what.
With regards to obstructions, both the Highway Authority and Police have powers to remove obstructions and prosecute the offender.
With regards to "an example of that regulation being used in the successful prosecution of the driver", all I would say to that is that I never got involved in this area of enforcement, but the guy in the opposite corner of the office did the actual enforcement. If it was within the remit of us as the Highway Authority then we would pursue it, otherwise we referred it to the Police.
We had a direct contact to the local nick, and when a vehicle was reported to us blocking any drive, in out, or in any circumstance where use of the drive was prevented, then we would request immediate attendance (which would be provided depended on the circumstances)
From our work with the Police I know that the regulation I cited was the one used by the Police for the obstruction, but there may of been others. If it went to court and the case was proven - ie the homeowner could not get onto his drive due to a vehicle blocking it, then the case was proven.