I think given that June had said she wanted her friend or family member to pray for Sheila and asked for someone to come and form an opinion of her health as he was so worried, June knew Sheila was heading for another breakdown, and the person who was sat at the table and said Sheila was very quiet an blurted out all people are evil and should be killed, they knew something was brewing.
Jeremy Bamber is in prison because he would have inherited. Once his mam and dad were killed, there was nobody to protect him from Robert Boutflour and his daughter. His daughter had already labelled Jeremy as a 'threat' (to their livelihoods)
prior to the killings. This is a very telling event (IMO) - as it clearly marks Jeremy's card. Some of Jeremy's own behaviour has simply reinforced the relatives' suspicion of him. The result being -
anything that could be gleaned from events that pointed towards Sheila was dismissed. Everything that could be interpreted as pointing towards Jeremy was soaked up and fed upon in a kind of frenzy.