Regulations and standards affect the specifications of bikes (and other configurations of pedal cycles) that can be sold and used on the roads.
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It is illegal to cycle on a public road after dark without lights and reflectors. Exactly which lights and reflectors, where to fit them and when to light up, is defined by the Road Vehicles Lighting Regulations.
Have you ever seen some pedal-powered contraption and thought: surely that isn't allowed on the road! If it has two brakes, it probably is, but here's where to find out for sure.
The Pedal Bicycles Safety Regulations (PBSR) are intended to ensure that new bicycles are safe when sold.
When you cycle into another country, your 'temporarily imported' bike doesn't have to be exactly like the bikes of that country, provided it conforms with a very basic, internationally agreed specification.
This is the law that lets you have a small electric motor on a pedal cycle, and still use it just like a normal bike.
Standards are specifications for products and services. Usually they are voluntary, but they can always be referred to in deciding whether something is or was safe.