I believe that (in the UK at least), the relevant legislation for the original question is Article 21 of the Air Nav Order (2000). Para 5 covers the specific point and reads as follows - the conclusion being that no pax can be carried on a training sortie:
(5)
(a) Notwithstanding the provisions of paragraph (1), a person may, unless the certificate of airworthiness in force in respect
of the aircraft otherwise requires, act as pilot of an aircraft registered in the United Kingdom for the purpose of undergoing
training or tests for the grant or renewal of a pilot's licence or for the inclusion, renewal or extension of a rating therein
without being the holder of an appropriate licence, if the conditions specified in sub-paragraph (b) are complied with.
(b)
(i) No other person shall be carried in the aircraft or in an aircraft being towed thereby except:
(aa) a person carried as a member of the flight crew in compliance with this Order;
(bb) a person authorised by the CAA to witness the aforesaid training or tests or to conduct the aforesaid
tests; or
(cc) if the pilot in command of the aircraft is the holder of an appropriate licence, a person carried for the
purpose of being trained or tested as a member of the flight crew of an aircraft.
(ii) The person acting as the pilot of the aircraft without being the holder of an appropriate licence either:
(aa) within the period of six months immediately preceding was serving as a qualified pilot of an aircraft in any
of Her Majesty's naval, military or air forces, and his physical condition has not, so far as he is aware, so
deteriorated during that period as to render him unfit for the licence for which he intends to qualify; or
(bb) holds a pilot's, a flight navigator's or a flight engineer's licence granted under article 22 of this Order and
the purpose of the training or test is to enable him to qualify under this Order for the grant of a pilot's licence or
for the inclusion of an additional type in the aircraft rating in his licence and he acts under the supervision of a
person who is the holder of an appropriate licence.