Nonsense.
Your logic applies to things like stanley knives, fixed and locking blades etc.
Penknives with a non locking blade less than 3" in length, do not require 'good reason' to carry on your person. There is a big difference between a penknife and a kitchen knife/machete/flick knife/screwdriver etc which might need a 'good reason' to counter such a proscriptive.
Granted, if you tried to use it as a weapon, to defend yourself or otherwise, it'd land you in trouble. But the issue is most penknives are tools - mine is the most useful thing I own and lives in my pocket no matter where I am (except when flying).
No honest copper is going to try for a conviction, for possession of a dangerous weapon, of the carrier of a UK legal penknife, without prior evidence of it being used as a weapon.
But in answer to the OP, you are not allowed to carry anything to use specifically for 'self defence' in the UK.