Well, one brake if it's a fixed and if you believe the CTC. Under our laws a bicycle must have a separate functioning brake on each wheel. The CTC maintain that a fixed wheel counts as a brake, although the law as written is unclear and I have never seen any case law to back them up. IIRC the law uses the word "separate" and as such I'm not sure a fixed wheel or a coaster brake would count as qualify since it is not separate from the drive system.
Given the number of people (kids and adults) round here riding jump and BMX bikes with no brakes at all with a freewheel I don't think this law is being actively enforced anyway.
As for the "track" description I used to get irritated by that, but it has been in common use as a description of any fixed wheel bike that I have become imune to it. Back in the day I used to have a fixed wheel MTB (proper 80's urban courier chic it was) and people used to call that a track bike. Brakes bar ends and everything else it had, but they still called it a track bike.