That figure is expected to rise, as fire chiefs do not expect to find any more survivors in the burnt-out Grenfell Tower in North Kensington.
The PM said people "deserve answers" as to why the fire spread so rapidly.
The first victim has been named by the Syria Solidarity Campaign as Syrian refugee Mohammed Alhajali, 23.
Six victims of the blaze have been provisionally identified, Metropolitan Police Commander Stuart Cundy said, but "there is a risk that sadly we may not be able to identify everybody".
Asked about the number of dead, Cdr Cundy said: "I hope it is not triple figures, but I can't be drawn on the numbers."