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The law specifies that direct drive (as in penny fathing or unicycle, cranks attached directly to wheel) is all the brakes you need. Otherwise you need two independent brakes, where a fixed wheel counts the same as a disc brake or rod brake.
You can get unicycles with hub gears and they come with two brakes on the same wheel (for obvious reasons).
I didn't check the definition of a brake, but imagine that's been tested! -
Yep.
http://www.legislation.gov.uk/uksi/1983/1176/pdfs/uksi_19831176_en.pdf
TLDR:
Bikes need independent brakes on the front and rear wheels (fixed counts on the rear).
Trikes can have two brakes on the front wheel.
In my research into the law if I remember correctly the letter of the law just says "two independent braking systems" the bit about different wheels has been inferred from independent, but never tested.