It would indeed appear that some ATC folks are not all that familiar with ICAO procedures....UK folks in particular.
No offence intended, but if you were to look into it a bit more, you'd find that the Chicago Convention is based on the principle of State sovereignty. Sure, the idea is that all States would employ the same rules in their national laws, but the "ICAO" system, as you put it, is just basically standard international law. The only way it differs from "normal" international law is that a standard in an Annex becomes binding on a State unless that State has notified of a difference. In a way this means that signatories to the treaty have committed themselves to following future changes to any Annex unless they positively say they're not going to implement the change.
This is why we have national variations in the way of doing things, and that's why the AIP is ever so important as you have to comply with the rules of any State that you're flying in/over.
So as far as the UK is concerned, they could have a requirement to report altitude/level passing when reading back a heading instruction if they so chose.