Well, apart from children having been already evacuated, there was everything from food vans to temporary accommodation, the rationing programme guaranteeing adequate healthy food & number of calories, provision of shelters, use of tube for deep shelters. Then the actions of the Red Cross & Sally Army. There had been planning for all this before the war, the Civil Service had geared up for providing for the civilian population and expected higher casualties anyway as the enemy was expected to use poison gas too.
But there were complaints, lack of shelters...the effect on the poor being greater than the rich (poor housing being near factories & ports)...
Civilans that could moved out of London, some to the dispersed factories.
It certainly wasn't all good - but Grenfell is bloody criminal.