The police should have picked up on the fact that he was the Grans toyboy
men who are interested in women a lot older than themselves generally are more prone some sort of mental illness, and looking at the state of the Gran one would have to agree he must have been some sort of nut.
The sniffer dogs werent ever taken in the house until the time the body was found apparently in the attic. The police are now apolgising blaming human error!! WTF obviously there lining someone up for the blame!!
Alternatively, as Tia's body was found in the loft, they could've passed her body from the neighbour's loft into the grandmother's if there isn't a wall between them, without being seen by the police standing guard outside.