British Prime Minister Theresa May apologised on Wednesday for the state's failure to support those people who survived the massive London tower block fire, and the government secured its first tranche of new homes for displaced residents.

The chief executive of a London borough where a tower block fire killed at least 79 people in Britain's worst blaze since World War Two resigns.

London police says 79 people are dead or missing presumed dead after a devastating tower block blaze last week.

British police says that 58 people are now assumed to have died in this week's blaze at a London tower block.

Fire engulfed a 24-storey housing block in central London, killing at least six people and injuring 74 others in an inferno that trapped residents as they slept.