She said the terms of reference of a public inquiry into the blaze were being drafted, and the government had now contacted all local authorities in England asking them to identify any safety concerns in light of the tragedy.
Cundy warned that the toll of 79 people could change.
"Equally, there may be people who thankfully may have managed to escape the fire and for whatever reason have not let their family or friends or police know", he said. The investigation will include areas such as the construction, renovation and maintenance of the building and fire safety procedures, he said.
"Until we do that, we can not look at anything other than staying with the same advice".
Of those injured in the fire, 18 people remain in hospitals across London, nine of them in critical care.
While emergency services have been widely praised for their handling of the disaster, the government has been criticized for a slow and inadequate response, with Prime Minister Theresa May facing public anger for failing to meet residents during her first visit to the site.
The remnants of an exercise bike, an oven and washing machine point to the lives of residents in the moments before the blaze.
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