If you are flying as pilot in command on your own licence, the primary liability is yours. If flying with an instructor, the primary liability is the instructor's. If flying solo but as an unlicensed student under the supervision of an instructor on the ground, the primary liability is yours, but a claimant might seek to establish that the instructor (and through him, the club), was negligent in signing you off solo. In addition, the aircraft owner has a liability for damage to people or things on the ground, but not in the air.
See also
http://www.pprune.org/forums/showthr...threadid=79560