HD
The ICAO convention rules are not applicable to military flights although the military, as a politeness and also dependent upon the countries involved, adhere to ICAO standards otherwise they fly Due Regard.
The Military are not signatures to the ICAO convention. In essence, so long as they remain over international waters, i.e. 12+ NMs offshore, they can fly where and when they like but with countries that have some political clout they don't, they adhere to the ICAO rules.
An example would be in the Gulf States where there is much military flying. They, the Military, would often fly in the approach lanes to Dubai International at any height that suited their operation up to 12 NM offshore. When questioned as the the lack of safety involved in such practice they would say that they are flying Due Regard and are over International waters. They are correct much to the chagrin of both the UAE ACC and OMDB APP controllers.
The fact that the Military behaves itself in Europe is that most European countries have access to the corridors of power and have corresponding gentlemen's agreements. That is why it doesn't happen in the Thames Estuary!