A few years ago, a boarding school with which I am connected lost one of its houses to fire at the start of the summer holidays. By the beginning of the Autumn term a fully equipped temporary structure, based on container-sized modules, and offering better accommodation than the 1920s building that had been destroyed, was up and running on one of the playing fields. It was used for 2-3 years until a new house was built. It was all arranged in collaboration with the insurers.
Mutatis mutandis, I cannot see why this could not be done on this occasion. There may not be much space in the borough, but Grenfell Tower is very close to Wormwood Scrubs Common, in Hammersmith and Fulham. There would be room for the entire community. I would hope that the suppliers of such modular units have already suggested something like this to the Council.