It is not Commercial Air Transport so have a look at: NCO.GEN.135 Documents, manuals and information to be carried. That will cover Private and Instructional flights.
...in the UK from 25th August 2016 in accordance with
Information Notice 2013-185 as the UK has applied the full derogation period for Part-NCO. At the moment ANO Article 150 and Schedule 9 apply to non-CAT flights.
Documents to be carried
150 (1) An aircraft must not fly unless it carries the documents which it is required to carry under the law of the country in which it is registered.
(2) Subject to paragraphs (3) and (4), an aircraft registered in the United Kingdom must, when in flight, carry documents in accordance with Schedule 9.
(3) Paragraph (2) does not apply to an EU-OPS aeroplane flying on a commercial air transport flight.
(4) If a flight is intended to begin and end at the same aerodrome and does not include passage over the territory of any country other than the United Kingdom, the documents may be kept at that aerodrome instead of being carried in the aircraft.
ifitaint...