non-pilots manipulating the controls isn't specifically prohibited
See article 50 of the ANO and some of the following articles. There is an argument that a person manipulating the controls of an aircraft is piloting it (even if under guidance and only temporarily) and a person 'piloting' an aircraft must hold an appropriate licence unless undergoing training for the grant etc of a licence. Whilst there is no definition of 'pilot' in the ANO why would you need the exemption for student pilots, if you could simply designate them as 'students' and not qualified pilots? The OED definition of a pilot is 'a person who operates the controls of an aircraft'.
The ANO provides:
50 (1) Subject to paragraph (2), a person must not act as a pilot of an EASA aircraft that is registered in the United Kingdom without holding an appropriate licence granted, converted or rendered valid under the EASA Aircrew Regulation.
(2) A person may act as a pilot of an EASA aircraft without holding an appropriate licence granted, converted or rendered valid under the EASA Aircrew Regulation when undergoing flying training, including solo flying training authorised and supervised by a flight instructor, in accordance with the EASA Aircrew Regulation as amended from time to time.
50A (1) Subject to articles 51 to 60, a person must not act as a member of the flight crew of an aircraft to which this paragraph applies without holding an appropriate licence granted or rendered valid under this Order.
50A applies to the member of the flight crew of an aircraft; flight crew includes a pilot and a similar exemption as to training applies.
If you carefully read the wording of the CAA advice you will get some idea of the potential problem. Article 50 is brought to you by the wonderful people at EASA and I suspect that the CAA are sensibly skating around it as strictly the regs would prohibit, for example, such things as letting your children or spouse handle the controls when you take them flying.