Breach of the peace has a specific meaning. It applies where harm is done, or threatened to be done or likely to be done to a person or in his presence to his property. The cops don t usually know this. It does not mean just making noise etc. If the cops say there is a breach of the peace, try to find out who they think is being harmed, threatened, likely to be etc.
Public highways are roads, pavements and dedicated rights of way.
This does not include private property. Remember land in front of buildings is often private, even if sometimes it looks like the pavement. The crucial thing here is that the cop must be acting in the course of his duty. This does not mean everything a cop does. For example if you are told to move and you refuse, you cannot then be obstructing a police officer in the course of his duty if there was no law requiring you to move in the first place.