Hello,
Ref: I am a UK Met Police Officer for what it's worth
Assuming the person from the dump finds the body, there's a question about how is it found.
If there's a nasty smell, but the bodies not been found, etc you'll get a call to police from dump, then a team response officer will attend. They'll most likely find the body, and call a scenes of crime officer (SOCO down)
At this point it's very non specialist, as the officer attending, based on experience may never have dealt with a dead child before etc, its possible that he/she will put body out before realising what they've got and that experts need to be called in. / throw up depending on smell.
You will then have the matter be referred to CID / the detectives.
If the death was not suspicious, it wouldn't be implausible for another/same team officer to attend, to give a death message of 'person has passed away.' (try and avoid saying 'x is dead'.
RE in the case you've described, you would have detectives allocated the case. All things depending, you could have the father be a named suspect for the case, at which point a arrest enquiry would be made, and response/community officers go around to arrest and take him to custody, where detectives will interview. Otherwise, you can have the detectives go around and do the arrest themselves.
You have interesting interactions with the law here, an arrest enquiry you don't have a warrant, so rely on your normal powers of entry, you generally knock on the door, they answer you say you're under arrest. A warrant, allows you to kick the door in and drag them out. But a warrant requires you to go to a court, which requires a certain amount of evidence. Section 17 PACE 1984, does allow you without a warrant to kick the door in TO execute an arrest, for an indictable offence (ergo murder) but you need to evidence that you know that they're in there. You can't be like, i used Section 17 to kick the door in, went in, oh he wasn't there, and then I searched the house whilst I was there.
If the father walks in smoking a joint, it really depends on the borough/officers attending. If your detective is a main character he may have a reputation for dealing with all crimes. However, detectives/officers generally tend to be extremely overworked, and I wouldn't bat an eyelid if the officer in question said "Sir can you put your cigarette out" and left it at that.
It should be emphasised that arrest itself is a investigative tool, it is not a form of justice.
Ergo, you have to demonstrate why the arrest is necessary and why you couldn't just invite them in to be interviewed by appointment. The usual one: "prompt and effective investigation" doesn't apply as its 4 years old... You're going to be looking at, the arrest is necessary for a promt and effective investigation NOW because without arrest he'll destroy evidence etc now he knows it's being investigated etc, or to stop him killing other people.
ID COP PLAN Flashcards | Quizlet (is your list of reasons)
After interview, he will either be: Charged, no further action or released under investigation. In this case, I would imagine he'll be arrested, then with a lack of evidence, released under investigation. The Released under investigation can be for a very long time.
(regarding the turning up to do the ID, it's likely that he'll already be ID'd if you want to turn up to arrest the dad at the same time. It would be more plausible if you turned up to do the ID, all goes well, then later evidence emerged meaning you went back to nick the dad.
The reason I say this, is if your going around to bust the dad, you already know it's his kid, so no ID is needed. There is a difference between a death message, informing someone that they're person is dead and a formal ID..
But if I'm honest, i've done death message but not ID being a humble grunt
If there's anything specific I can help you with please ask, but I'm not a homocide detective.
Where is your story set, as Met will be very different to County forces.