From experience of operating a private aircraft.
As long as the gentleman or company owns the aircraft and that the only money exchanging hands is your costs then that is absoutely fine.
No AOC is required.
All you need to do is ensure that you or the company / owner can demonstrate that "no profit" is being made for the flight. Just enure you keep a paper trail of costs paid; i.e direct operating costs.
Just so you can read yourself, Google "CAA Public Transport Summary" this is a very useful document and will explain it more clearly.
Hope this helps.