^^^Agreed.
Here's the manual testers must work to:
https://www.gov.uk/guidance/mot-inspection-manual-for-private-passenger-and-light-commercial-vehicles/8-nuisance
Clicking on 'Exhaust emissions', and then scrolling well down takes you to 'Engine malfunction indicator lamp (engine management light or ‘EML’)', where the tester is given this instruction:
"Turn on the ignition and check that the engine malfunction indicator lamp (MIL) illuminates and then goes off. On some vehicles it will be necessary to start the engine before the MIL goes off".
The table of defects below that then shows that an engine management light which fails to extinguish once the ignition has been turned on (or once the engine has been started) is classed as a 'Major' fault.