every piece of police code quoted so far goes to show that its only allowable without a warrant for an indictable offence, which isn't what you are talking about.
Again I'll say, the power you suggest they have is completely and totally unlimited as without any arrests, or basically anything they can enter anyones house under the pretense of looking for someone they do have an arrest warrant for. That is clearly ridiculous, it clearly doesn't happen in this country, so what you've suggested is just completely wrong. This to me says you don't know what you are talking about on the subject matter.
I don't know either, I'm not a cop, but based on the actions of the police its very simple to see you're wrong.
Its this simple, there are lots of law's in place limiting the powers police have for the exact reason that they can't just make up a pretense and enter any ones house. Hence the need for warrants, by the way you've said it can happen, you find out about a house that drugs are sold in, search everyone who comes out, the first person they arrest with drugs lets you go in and search the house and jobs done, investigation over, drugs siezed and everyones in jail. The very fact that it doesn't happen, proves you are wrong. The fact that investigations like that take time and effort and need warrants to go in and search proves you are wrong.