All you need is for the Head of Training to say don't fly as PIC from the right seat with passengers and that then becomes a legal requirement if you want to fly that aircraft.
As for the legal position - aside from being told not to there is no direct contravention - even if you are not an instructor.
However, imagine you in court answering an allegation of manslaughter;
Mr. freeasair can you please prove that you were not giving unauthorised instruction?
The designer of the aircraft has gone to great lengths to ensure that various critical instruments and warning lights are placed in the view forward of a person sitting in the left seat. Would you not agree that flying from the right seat requires increased vigilence and effort on your part with regard to maintaining especially a safe airspeed in a critical situation and would you not agree that the average safe pilot would prefer to when possible mitigate against any risk.
As an instructor (produces the CAA AIC etc, Accident report from the Bournemouth accident) you will be aware that where there is no instruction taking place, there is no requirement for you to sit in the right seat and therefore if you were acting in as safe a manner as possible you would have choosen the left seat which made observing the critical instruments easier and would to the average lay person clearly have improved the safety of the flight.
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It is a sad fact of life these days that most of our efforts go into avoiding having to answer such questions in court!
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However, there are a few important questions that may also be asked - 1 passenger paid 100% of the costs. How do you square that against the legal requirements regarding not for reward. You were rewarded quite well by that student.
Without an adequate explanation (prior knowledge - where I would say fly from the left) I would be giving you your P45 if I was the HoT. I have no way of knowing that you are not short cuting the school and giving some instruction on the side using the school aircraft and receiving compensation direct from the student. This especially so if there is both dual / solo hire rates.
Why could you not have shown the student a perfect flight as flown from the left seat and given good explanations / demonstrations of what they need to do? After all as an active instructor it is usual to have plenty of right seat time but very little left seat time.