In the UK, IFR flights outside controlled airspace are
required to adopt quadrantal level when flying above the transition altitude and below FL245. Above FL245 in uncontrolled airspace IFR flights are
required to fly semi-circular levels (but try finding some of that
).
In most other states, VFR flights are
required to fly at the semicircular + 500 ft levels. The criteria for application vary, but it's typically 3000 ft amsl or 1000 ft agl, whichever is higher. This is not a requirement in the UK -- outside controlled airspace VFR flights are
advised, but not required, to adopt quadrantal levels.
IFR flights in controlled airspace are required to fly at whatever level is specified in their ATC clearance.
Conventionally, levels are assigned according to the semi-circular rule unless on an airway notified otherwise. Whether
rules as such exist within the ATC framework to enforce that is beyond me as a mere pilot
to say with certainty, but my understanding is that they do not.