I probably read too many police procedural novels, but here goes...
When an adult goes missing there are some key factors for the police... what do they take with them, have they used their phone, have they accessed their bank account or used their bank cards anywhere... After a week or so of no apparent signs of life, they very quickly assume the person is likely to be dead.
The waters may have been muddied with Helen since early on we thought she had access to a four figure sum of cash in the house. We never heard much more about this so what happened to that info, where it came from and how they discounted it, I don't think we know.
As all good sleuthers know, the last person to see the victim and/or the partner is always the prime suspect. So LE will have been watching IS from the very beginning.
They can only arrest someone when there is enough information to justify it. I guess it took them that long to feel confident they had the right person in their sights, probably based on all the little pieces of info slotting together, from her lack of apparent signs of life, his story full of holes, the router data, Helen's family and friends saying there was no way she'd vanish and not contact anyone, the dog alerts at the house, the lack of sightings of HB and B, the presentation of IS (emotionless except when it came to his own discomforts, speaking of HB in past tense, going on holiday when HB could supposedly come home at any time etc etc). There may be lots of things we don't know about that were not strong enough evidence to form part of the prosecution case but were useful for the police's decision making.