While I haven’t checked, I would be highly surprised if the police didn’t have the necessary powers to knock on ones door, irrespetive if someone places a sign or not. When it comes to entering the property to obtain evidence or determine if a past crime has been committed, this is a different matter. If a crime is in progress (such as domestic violende), then I would expect they would also have the necessary powers to enter to prevent the crime/continuation of the crime. Not doing so goes against the basic principles of policing.
Hypothetically, if a seller was having a heart attack and knocked on your do not knock door, then I expect they wouldn’t be trepassing as the purpose of the knock is not to sell you something but to save their own life. If one didn’t answer, then this is something one would have to live with for the rest of their life.