So long as the student is receiving instruction from a qualified FI then they are legally a student, and the FI is exercising the privileges of his licence and rating. If remunerated, it is Aerial Work not public transport. There is no legal requirement to be assigned to any particular body or organisation to do this other than a "flying club" which could be just two people, the FI and the student.
"Registration" is a JAA requirement which has no legal standing in the UK. It may affect the students ability to be issued with a licence, but it does not undermine the privileges of the instructors rating.
The original question related to the legality of the trial lesson, not how to go about training the student for a licence or rating.
There are a good many trial lessons to Le Touquet for lunch whilst the FI does exactly that! It may be more attractive than Birmingham or Bristol.