Every time I have gotten an Uber in London the car has been a Toyota Prius, I don't know if that particular car is still congestion charge exempt but even if it isn't what's to stop minicabs all starting to drive vehicles which are exempt?
They are licensed. Licensed minicabs of any type are currently exempt, I believe. The rule could simply be that all minicabs are subjected to the fee, it'd be enforced by license plate as it is for other motorists.