There are two levels of law-breaking in the Highway Code:
- 'MUST/MUST NOT' in the Highway Code means you must obey the referenced law. That 'MUST/MUST NOT' is black & white.
- 'should/should not' means a more general driving law may be applied such as that of 'driving without due care and attention'* or 'dangerous driving'*, if the police deem it appropriate.
As flecc says, and regardless of which variant above, whether you actually get fined depends on being spotted, the outcome of your action (nothing, injury, death), repeated offending, how overloaded the police are, and how polite/apologetic/rude/pig-headed/entitled you are.
In the case of the van + bicycle collision, there's no specific law being broken by either party (i.e. a MUST/MUST NOT rule), but I'd suggest the cyclist was 'driving without due care and attention' - "At junctions with no separate cyclist facilities, it is recommended that you proceed as if you were driving a motor vehicle". The van driver may also be partially at fault if that crossing was deemed to be a cycle way but the road markings suggest is isn't.
In the case of the car + near miss again it isn't a MUST/MUST NOT rule, but this time it's the car that's 'driving without due care and attention' - "Give ... cyclists ... at least as much room as you would when overtaking a car". Combine that with 'how polite/rude you are' and you can see why the car driver is being held up as a example. The motorist believed he was in the right - he tested the law, and lost, so maybe not 'rude' - just pigheaded or entitled.
*Some examples of offences here, when you expand the sections: