I'm not sure this is entirely representative.
Yes Police had been told Jeremy had called through the call, and that his sister had gone mad etc etc.
So it's perfectly rational, at the scene of the crime, finding the bodies and sheila holding the gun etc etc to still buy into this story.
It's been noted that SOME officers thought something wasn't quite right, but this has to be put down to hearsay really (until officially proven).
So, the real problems didn't start then - they started when the 'gathering of evidence' didn't wipe the slate clean of all assumption, but continued to assume 'it must be true'.
For whatever reason (trying to minimise the impact on the family / good taste, or trying to cover something up) the Police did the basics, but no more than that.
In the meantime, SOME family members started raising questions. Not all of them. And it's probably unfair to say they didn't know the family well. They were Aunts and Uncles (largely) of Jeremy and Sheila and arguably would know Jeremy better than Colin Caffell.
It could be argued that Colin most likely knew Sheila best (other than Jeremy, June or Nevill) and it could be argued that Julie knew Jeremy best other than Sheila, June or Nevill) - it's a very subjective topic about who knew who best, but I don't think it's reasonable to think Jeremy wasn't particularly well known to them - they'd have seen him growing up, but as a young man, Julie would have become closer to him, obviously.
Anyway, regardless of that, the relatives didn't stand to gain much at all - at least not directly, BUT there were complications where yes, some of them would benefit. There's certainly a motive there, but not quite as 'we get all the money if we frame him' style.
There's a motive for Mugford too.
A motive for Sheila
and a motive for Jeremy.
Now if the family set out to frame him, OR add to the evidence, because they thought he was guilty anyway, then they would still have to get Mugford on their side too and invent a lie. OR they got very lucky and Mugford lied as a result of her grudge too.
So it took two distinct parties to either collude, or BOTH independently want to frame him.
Given the family's suspicions, and yes, prodding the police to take it more seriously AND finding the silencer, the police where then forced to start looking at Bamber.
They COULD (and some say DID) try not to investigate too hard, because they had already assumed suicide and didn't want to look bad, or didn't want to stir up trouble in an already broken family. However, in the end, their hand was forced and they started investigating / watching Bamber.
Bamber may very well have been grieving 'in his own way'. And if that way meant weekends abroad with Julie, or being fairly lavish with money, so be it.... BUT, it did little to give the impression of being grief stricken. Nor did his auctioning of items from the farm and from his sister's Maida Vale flat.
There's nothing wrong with what he did. It doesn't make anybody guilty for clearing out a flat of valuables and selling some, BUT as stated earlier, it certainly doesn't look great (and yes, I can hear the argument that says if he was guilty why would he draw attention to himself like that?).
Now, as all this was starting to unfold, the police where doing forensics on the gun and the bodies.
It's here where the suicide theory started to look a little less strong (but NOT disproven) - the absence of residue on her hands that would normally be associated with firing 25 rounds and loaded a gun at least twice). A seeming cleanliness to her feet that didn't seem as though she'd wandered around a house and massacred 4 others. Two wounds to her head/neck which whilst possible to survive one, still seemed 'unusual'.
Then there was the silencer and the blood on and within it, found put away downstairs.... perfectly possible to do with Sheila's injuries (IF she was still able after her first shot)... and the seeming "unusual thing to do, put away the silencer before killing yourself".
There was Jeremy's calls which he couldn't prove, and calls to Julie that could be proved, but the contents of which only known by Jeremy and Julie...
If you take any one point, it can be explained away - Sheila washed, that's why she was clean. Sheila shot herself, moved around a bit, then shot herself again. Sheila was seen on the kitchen floor, woke up, moved upstairs when the police were in the house and then shot herself etc etc...
But when you try to add them all up, the chances of them all happening get slimmer and slimmer each time.
I have to say, it's perfectly possible that numerous 'unlikely' events can all happen on the same night and afterwards - just because it's a million to one, doesn't mean it can't happen.
The vast majority of the evidence against Jeremy isn't forensic. There's actually nothing to put him at the scene. The forensic evidence is more geared towards suggesting Sheila didn't do it (than it is towards Jeremy having done it).
Jeremy therefore becomes the prime suspect by default - since there are only two ways he could know about the trouble at the farm - a) Because sheila did it and all that Jeremy said was true..... or b) He did it, or knew who had (hitman).
The evidence probably gave (say) a 60% jeremy did it, and 40% sheila.
What ultimately finished Jeremy off his actions after the deaths (which in themselves don't make him guilty) AND Mugford's testimony that he'd told her he hired a hitman.
The actions of Bamber after the deaths probably tipped the balance of guilt to 75% Jeremy 25% Sheila.
The 'confession' as told by Mugford shifted it again to 95% Jeremy 5% Sheila.
seeing the photos at the trial, and the anecdotal witness statements AND manner of Bamber in general (self assured, cocky) probably put the odds at 99% Jeremy, 1% Sheila.
The jury returned a verdict of guilty by a majority of 10:2, so all in all he did quite well - just not well enough.