In the UK, bikes operated on public roads must have two independent braking systems, one for each wheel, in "efficient working order". Fixed gearing counts as a braking system, so a fixie is only required to have a front brake, but a single-speed with only one brake (or a bike with only a rear coaster brake) would not meet the regulations. 

Ref: http://ukcyclerules.com/2011/05/04/the-rules-of-bike-brakes/