An aircraft operating crew must hold the appropriate licences (except for military crews in the course of their military duties), except for:
1. Radio operation by glider pilots or pilots under training.
2. U/T pilot flying solo for qualification purposes.
3. U/T pilot flying dual for qualification purposes with a FI.
Hence you may only log the flight time of which you speak as passenger flying. - if at all. I should keep quiet about it, if I were you, as if you've done a lot of this unapproved flying someone in officialdom might wonder what has been going on. For example, if you went flying in a C150 and operated the controls whilst your PPL chum poked a camera out of the side window to photograph people's houses, you could certainly anticipate A Visit....
If the aeroplane was hired to your non-FI friend and he/she allowed you to handle the controls, the aeroplane insurance was probably invalidated.
Lastly, a 'Q'FI is a military flying instructor. Civil instructors are either FIs, (Flight Instructors), or FI(R)s (Flight Instructors with Restricted privileges); however there may still be some 'Assistant Flying Instructors' (AFIs) around.