Scotland Yard on Monday confirmed at least 79 people perished in last week's blaze in west London but said it may not be possible to identify all the dead due to the intensity of the fire in the wealthy Kensington and Chelsea borough.
"His family is being supported by liaison officers from the Metropolitan Police", Cundy said.
The investigation will include areas such as the construction, renovation and maintenance of the building and fire safety procedures, he said. Authorities may never be able to identify some of the victims, he said. For police, fire and emergency crews inside the tower, "it is incredibly emotional working in there", Cundy said.
Families who have lost their homes must be supported, grieving people must be helped and it must not be "so hard" for those who need help to find it, he said.
Around 70 people are missing, according to Britain's Press Association, and identification of the victims is proving very hard. "There is also a real possibility that there may be people in the building that no one knows are missing", he added.
Speaking outside after the service, which he attended with his wife Saadiya, he said people are "angry not simply at the poor response in the days afterwards from the council and the Government, but the years of neglect from the council and successive governments". Clement's Church near Grenfell Tower.
A minute's silence was held across Britain 11am local time to honour the victims of the fire.
"The awful reality of the fire that night means that we are supporting some people who may have lost a number of members of their family on that night", Cundy said. The investigation will identify any criminal offence that has been committed.
In a report, BBC said the number could be around 70 people in total.
The fire has prompted warnings about fire safety risks in many other council tower blocks built in the same era.
Footage recorded from inside a fire engine making its way to the Grenfell Tower fire shows the shock and disbelief of firefighters as the scale of the blaze becomes apparent.