A bit late to the party (see what I did there?), but:
* A driving licence is just that: A licence to show you're considered competent to pilot the types of vehicles listed on it, having done some mandatory training and passed the necessary test.
So: Driving a motorised anything is done "under licence".
* This licence can be revoked if you break the relevant laws you agreed to when it was issued.
But: Riding a bike on the highway (in the U.K.) is done by RIGHT. Similar to the rights of pedestrians and horse riders to use the Queen's Highway without hinderance.
So, as it's effectively a "right of passage":
* There's no mandatory training nor test nor licence before you can ride a bicycle;
* There's no mandatory helmet law or similar (in the U.K.)
* And there is no lower (or upper) age limit to ride a bike.
* There's no way you can be banned from doing it (such as having your licence revoked).
Usually, one single "motor vehicles" licence covers all of them. So if you commit an offence on your motorbike it goes on your combined car/ motorbike/ truck licence.
But, because it's quite possible to cycle without having any other sort of licence (like with young kids who are too young to drive, and; because cycling is by "right" not by "licence")
This means that the law CAN NOT make a link between riding a bicycle and having offences or penalty points added to your "motorised vehicles" licence.
But, due to 1890s "Scorchers" etc. scaring pedestrians, you CAN be fined for "cycling furiously" and otherwise being a bit of a public nuisance.
And, like Scant's mate, you CAN be fined for breaking traffic regulations (like jumping red lights) but The Man could never transfer that onto a licence of any sort as penalty points etc. cos there's zero link between the two.
Basically, the law only really goes after cyclists if you do something in traffic that would put yourself or other people at risk.
As mentioned - it's mainly because nobody likes scraping up the remnants of ex-cyclists off the road.
Drinking and cycling is self-limiting, anyway, as you tend to fall off.
But not as rapidly as drink-skateboarding, which really IS asking for trouble [cough!

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