Just as an aside, since clearly the infringements mentioned are different circumstances, the presence of an ATZ without ATC means that you can still legally fly within it, since neither a FISO nor the airfield operators have any power to prevent access to ATZ airspace.
Having said that, the pilot has to ensure that they comply with ANO Rules of the Air Article 39. Amongst other things, this means they would have to obtain aerodrome information from the FISO to enable them to conduct a safe flight within the ATZ.
The judgement and airmanship then exercised based on the information passed is up to the pilot involved. It would also depend on the quality and quantity of the information given as well. Being told of an air display would on most occasions make a pilot be wary of routeing near the airfield, however, if told the display currently taking place was by a low and slow aircraft remaining close to the airfield, AND you had the aircraft in sight, then you might judge flying a suitable distance from the observed activity is 'safe'.
If there is Restricted Airspace (such as a Red Arrows TRA), then you have no excuse for entering and cannot legally do so, except under any conditions related to the specific TRA. Was there a TRA at Old Warden during the 'alleged' infringements ??