I don't think it's about politeness. Warning about the smell is polite, but I think it's simply logistics holding them up at the moment. They'll have to gather the right staff for the job, build the walkways, figure out a production line method for grabbing bundles of waste and then sorting through, bearing in mind that it'll have to be done in a forensic fashion, and I would have thought a full forensics team would have to do the fine sorting to look for things like clothing fragments and small bones that most people wouldn't recognise for what they are?
Unless I'm completely wrong about that last part, I don't think you'd often get that many forensics officers in one place at a time, so they'll have to be called in from other counties or from the Met?
I don't think this is a warrant situation. It's still a missing person's inquiry, so the company that own the landfill have probably voluntarily cooperated to close that section down, and they're probably voluntarily allowing the search. There might not be a strong evidence trail that Corrie is at the landfill...it might just be that's the only thing left that makes sense after searching roadsides, fields, rivers, etc.