Residents of Trellick Tower, a 1972 public housing block, fought to stop a development project they said would undermine the building’s integrity. But they fear the reprieve might be only temporary.

It stands 393ft high. A brutal mass of concrete and glass ­reaching up to the sky, designed as the answer to modern-day living. Trellick Tower opened in 1972 and was seen as the ultimate in high-rise ...