LONDON — With the death toll from a horrific London fire rising and many residents still unaccounted for, Prime Minister Theresa May — under pressure from critics — on Thursday ordered a formal inquiry into the disaster that turned an apartment tower into a smoldering ruin.

At least 17 people are known to have died in the blaze at Grenfell Tower, which began in the predawn darkness on Wednesday, but that figure is certain to climb, the authorities warned. As of late Thursday afternoon, 30 people remained in hospitals, including 10 in critical condition.

A senior police official, Commander Stuart Cundy, said of the death toll, “I’d like to hope that it isn’t going to be triple figures.” Even as investigators with search dogs combed what is left of the building, safety inspectors were conducting checks at other high-rises.