It's not the IEEE who publish regulations. It was the IEE now called the IET.
The regulations cover a huge range from domestic to large factories so the wording has been very careful not to have a regulation to stop something which makes sense in industry even if not when when applied to domestic.
The Guide to the BS7671 (17th Edition) tends to be more down to earth.
Twin and earth is not classed as a flexible cable and should not be flexed and where it is clipped then this also gives mechanical retention of the cable. Without clipping any junction boxes would need a device for mechanical retention and this is normally where the problem lies.
521.5.1 Electromechanical stresses
Every conductor or cable shall have adequate strength and be so installed as to withstand the electromechanical forces that may be caused by any current, including fault current, it may have to carry in service.
522.6.1 Wiring systems shall be selected and erected so as to minimize the damage arising from mechanical stress, e.g. by impact abrasion, penetration, tension or compression during installation, use or maintenance.
522.8.1 A wiring system shall be selected and erected to avoid during installation.. use or maintenance, damage to the sheath or insulation of cables and their terminations.
522.8.5 Every cable or conductor shall be supported in such a way that it is not exposed to undue mechanical strain and so that there is no appreciable mechanical strain on the terminations of the conductors, account being taken of mechanical strain imposed by the supported weight of the cable or conductor itself.
522.15.1 Where risks due to structural movement exist (CB3), the cable support and protection system employed shall be capable of permitting relative movement so that conductors and cables are not subjected to excessive mechanical stress.
526.1 Every connection between conductors or between a conductor and other equipment shall provide durable electrical continuity and adequate mechanical strength and protection.
526.6 There shall be no appreciable mechanical strain on the connections of conductors.
The list goes on and without seeing the installation to work out if it does not comply would be hard. For example 522.15.1 could mean that to clip the cable would be against the regulations.
With all sockets under 20A and most wires buried in walls or similar now being RCD protected in real terms unlikely to present a danger. Also with the requirement for work in kitchens to be notified to the LABC normally through the electricians scheme provider which means they have to fill in a minor works or installation certificate saying what they have done it is unusual for electricians to leave them selves open to loosing there ability to self certify by doing sub-standard work.
As long as you receive the completion certificate then it is unlikely there is anything untoward as inspectors do select random jobs and so not doing to standard would likely mean big problems for the electrician or firm he works for.