Trial Flight and Introductory Lesson are just fancy names used to attract customers who are not initially coming with the intention of learning to fly.
A flying lesson is exactly that no matter what else you might call it, and can only be given by a person holding a Flight Instructor rating. If a person pays for a flight that is not a lesson, then its public transport and needs to be conducted under the auspices of an AOC. Flying clubs are exempt from the requirement to have an AOC solely for the purpose of giving lessons. Private flights are another issue, people who walk through the door and pay for a flight are not going on a private flight. Ask yourself a very simple question, would the flight still go if the said person did not pay to go on it!
There are numerous reports of unqualified pilots giving trial lessons, if they are caught the CAA will prosecute them if they can get enough evidence. Usually the punter doesn't complain, so its down to people in the industry to report such activity.