The Quadrantal rule is or UK UNCONTROLLED AIRSPACE ONLY.....look at any UK LO enroute chart in your JEPP manual...you will find 2 levels 'schematics'.

One for UK uncontrolled airspace, and one for everywhere else.
The 'everywhere else' schematic outlines the ICAO semi circular cruising levels - for tracks 000 - 179M ODD levels, 180 - 359M EVEN levels. This rule holds up to FL290....
If you now refer to a HI enroute chart you will find a different levels schematic.

This will offer the same rule up to FL290, and then a different rule at and above 290.

This is because the min separation above FL290 between opposing traffic increases to 2000ft (versus 1000ft below FL290).