The Red Cross in London is running evacuation centres for people who had to flee the 24-storey apartment building razed by fire.
Twelve people are confirmed dead and many people are unaccounted for.
Red Cross spokeswoman Penny Sessions told Rachel Smalley people are very concerned about friends and relatives.
"But we did trace a child who'd lost its parents and parent who'd lose a child, managed to put them back together, and in other cases it's just people waiting for information," she said.
"It will take time, it is a very distressing time."