And you most certainly would pay - unless, of course, the flight was in a Permit aeroplane whose Permit did not include use for flight instruction. The flight would then be entirely private. I've only done that once - but the applicant did pay for my fuel to drive to his aerodrome.
As I am certain you have more than 1,500hrs join us as an LAA coach and be paid within the CAA approved scheme for your expenses on permit aircraft.