It doesn't matter that you're a member of the club, if you're paying for the flight it is illegal.
The type of pleasure flight you are describing needs a cpl holder and an AOC, neither of which this club has.
To be a lesson, it requires someone with an instructor rating.
So unless this PPL holder has an instructor rating, the flight is illegal. If you pay for 100% of the cost of the flight, even if they dress it up as club membership, it is illegal.
How would you feel if you ran a taxi company, but someone kept turning up to the taxi rank in a private car and offered to take people home if they joined his club. He wouldn't have a taxi licence, or taxi insurance, so none of the over heads, but importantly none of the cover when things go wrong.
It's exactly the same here, without an AOC, you can not operate pleasure flights, without an instructor rating and authorisation you cannot operate a flying lesson, so just a PPL taking you up is illegal and if it all goes wrong you will find those friendly people you booked with denying all knowledge, and you're left with no cover at all.