The decision to prosecute or not rests entirely with the police force dealing with the offence.
However and generally speaking, the person supervising a learner driver does not automatically commit any offences the driver commits.
There has to be evidence of culpability by aiding, abetting, counselling or procuring, or inciting the commission of the offence. Even if the vehicle has dual controls and the instructor could have applied the brake, he/she doesn’t commit the offence just by failing to do so.
If the instructor has taken over and is controlling the steering wheel from the passenger seat and has dual control for the pedals, then the the instructor and not the pupil would be “driving” at that point in time and may be eligible for a course as part of the offence disposal process.
If not, consider contacting us.