From a Canadian perspective, the Queen/King (or their represtative) has a legal veto on any new Canadian laws. It has never been used.
How this applies to the UK, I'm not sure. How this veto applies to decisions of governance, I would say that it is a very weak political force.
Anyways, you seem frustrated at the current system and are looking for a solution.
My reason for being on Medium is to promote my alternative democracy.
Here is my TDG essay:
https://medium.com/discourse/tiered-democratic-governance-3f36a8f45660