Certainly only licensed or government aerodromes may be used for ab-initio PPL SEP training. But regarding a flight with a student to an unlicensed aerodrome for maintenance purposes, things are less clear. If, for example a flight from a licensed aerodrome culminated in a landing at an unlicensed aerodrome, I would consider that the student shall not be allowed to control the ac for flight within the unlicensed aerodrome circuit, including the landing. So the RF must not allow the student to log the entire flight, nor charge him/her for the entire flight.
Similarly, to fly with a student from an unlicensed aerdrome to a licensed one for instruction in circuit flying would mean that the student would have to be a non-paying passenger for that portion of the flight at the unlicensed aerodrome. It could be a cost effective option if the all-in cost (site rent, ac parking charges, fuel) to the RF were considered - but I doubt whether the Authority would routinely condone such activity.