Police have no authority to stop you for covering your face.
This is clearly bollocks. The police have the authority to stop anyone they like, for any reason (and for none) They can ask you for ID, for any reason (and for none) They can ask you to uncover your face. None of that is outwith their authority. The only thing they can’t do (without reasonable cause) is search you.
You do not have to comply with their requests, you don’t have to uncover your face, you can say no I don’t want to. They may ask for your ID and if they have a reason for doing so, they can state it and if you refuse, you are at risk of arrest. If you are aggressive, you risk arrest.
Your title is disingenuous but I suspect you know that.