(from a question) self-classification has no incentives for accuracy, in fact directly the opposite. Changing your classification over time to accurately reflect changing business strategy just adds paperwork.
e.g.
77220: renting of video tapes and disks
01440: raising of camels and cemlids
82990: other business support service activities (10%)
20% not classified
3 million companies in Companies House
Almost a million are unclassified or improperly classified.
This presentation / research did not attempt to classify these unclassified companies.