I'm sorry but again fecc , I don't read the regulation in that light.That article has this wrong comment by the BBC:
"By law, a bike on a public road in the UK must have two brakes.
A fixed-wheel bicycle has a single gear, no freewheel mechanism and dropped handlebars. The rear fixed wheel of a fixie - which a rider can slow using the pedals - counts as a brake."
The law specifies that a fixie with a front brake has one brake, and that it is legal, so it is incorrect to say every bicycle has to have two brakes. Nowhere does the law specify the fixie transmission is a brake. By inference from a further section it says the opposite.
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The regulation states very clearly that there be at least one braking system.
It then makes a distinction between fixed and free wheeling bikes. In the case of the fixie, it then requires that there be a brake fitted to the front wheel.
It explicitly states that where the pedals are fixed to the front wheel, without an intermediate chain as in penny farthing or children trikes, that would serve as a brake.
So it is at best silent on whether a rear wheel fixie, via or without a chain constitutes a brake. Somewhere else, on a bike forum, I picked up a reference, cannot confirm, that in a German court case, which requires two brakes, a rear fixie met the requirement of a brake.
As an aside, in Irish law, the offense of wanton and furious driving , which would have been carried accross from UK law was dropped from the statue books.